Samacheer Kalvi Class 11 Computer Science Solutions Chapter 2 Number Systems

Part - I

I. Choose The Correct Answer:

 

Question 1. Which refers to the number of bits processed by a computer's CPU?
(a) Byte
(b) Nibble
(c) Word length
(d) Bit
Answer: (c) Word length
In simple words: The 'word length' of a computer tells you how many bits its main brain (CPU) can handle at one time. This impacts how fast and powerful the computer is.

🎯 Exam Tip: Remember that word length is a key measure of a CPU's processing capability, not just any data unit.

 

Question 2. How many bytes does 1 KiloByte contain?
(a) 1000
(b) 8
(c) 4
(d) 1024
Answer: (d) 1024
In simple words: A Kilobyte is a unit of digital information storage. In computer systems, 1 Kilobyte is equal to 1024 bytes, not 1000, because computers use powers of 2.

🎯 Exam Tip: Always remember that computer memory units like KB, MB, GB are based on powers of 2 (1024), not powers of 10 (1000) as in the decimal system.

 

Question 3. Expansion for ASCII
(a) American School Code for Information Interchange
(b) American Standard Code for Information Interchange
(c) All Standard Code for Information Interchange
(d) American Society Code for Information Interchange
Answer: (b) American Standard Code for Information Interchange
In simple words: ASCII is a special code that helps computers understand characters like letters, numbers, and symbols. It is a standard way to represent text.

🎯 Exam Tip: Knowing the full form of common computer acronyms like ASCII is essential for basic computer knowledge.

 

Question 4. \( 2^{50} \) is referred as
(a) Kilo
(b) Tera
(c) Peta
(d) Zetta
Answer: (c) Peta
In simple words: In computer terms, \( 2^{10} \) is about a Kilo, \( 2^{20} \) is Mega, \( 2^{30} \) is Giga, \( 2^{40} \) is Tera, and \( 2^{50} \) is Peta. These terms show how big the storage or data amount is.

🎯 Exam Tip: Familiarize yourself with powers of 2 and their corresponding prefixes (Kilo, Mega, Giga, Tera, Peta, Exa, Zetta, Yotta) for various computer measurements.

 

Question 5. How many characters can be handled in Binary Coded Decimal System?
(a) 64
(b) 255
(c) 256
(d) 128
Answer: (a) 64
In simple words: The Binary Coded Decimal (BCD) system can handle 64 different characters. This is because it uses 6 bits to represent each character, and 2 raised to the power of 6 equals 64.

🎯 Exam Tip: Remember that the number of characters an encoding system can handle is determined by 2 to the power of the number of bits it uses ( \( 2^{\text{bits}} \) ).

 

Question 6. For \( 1101_2 \) what is the Hexadecimal equivalent?
(a) F
(b) E
(c) D
(d) B
Answer: (c) D
In simple words: To convert binary to hexadecimal, group the binary digits into sets of four from right to left. Each group of four binary digits then becomes one hexadecimal digit. For \( 1101_2 \), it directly translates to 'D' in hexadecimal.

🎯 Exam Tip: Memorize the hexadecimal equivalents for binary groups of four bits (0000 to 1111) to quickly convert between binary and hexadecimal.

 

Question 7. What is the 1's complement of 00100110?
(b) 11011001
(c) 11010001
(d) 00101001
Answer: (b) 11011001
In simple words: To find the 1's complement of a binary number, simply flip each digit: change every 0 to a 1, and every 1 to a 0. This quickly gives you the complement.

🎯 Exam Tip: For 1's complement, remember it's a direct bit inversion. For 2's complement, you first find the 1's complement and then add 1 to the result.

 

Question 8. Which amongst this is not an Octal number?
(a) 645
(b) 234
(c) 876
(d) 123
Answer: (c) 876
In simple words: Octal numbers only use digits from 0 to 7. Since 876 contains the digits 8 and 7, it cannot be an octal number. Any number with digits 8 or 9 is not octal.

🎯 Exam Tip: Always check if all digits in a number are within the valid range for that number system (e.g., 0-1 for binary, 0-7 for octal, 0-9 for decimal, 0-9 and A-F for hexadecimal).

Part II

Very Short Answers.

 

Question 1. What is data?
Answer: The word 'data' comes from the Latin word 'datum,' which means a raw fact. Data refers to basic facts about people, places, or objects. For example, 'Rajesh,' '16,' and 'XI' are individual pieces of data, which become meaningful when processed. Data is the unprocessed information that computers work with.
In simple words: Data is raw facts, like a name or a number, that don't have meaning until they are processed.

🎯 Exam Tip: When defining data, emphasize that it is "raw" or "unprocessed" and distinguish it from "information," which is processed data.

 

Question 2. Write the 1's complement procedure.
Answer: To find the 1's complement of a number, follow these steps:
Step 1: Convert the given decimal number into its binary equivalent.
Step 2: Make sure the binary number has 8 bits. If it has fewer than 8 bits, add leading zeros to the left until it becomes an 8-bit number.
Step 3: Invert all the bits. This means changing every 1 to a 0 and every 0 to a 1. This flip creates the 1's complement. For example, to find the 1's complement of \( (-24)_{10} \), we first convert 24 to binary, make it 8-bit, and then invert the bits.
In simple words: First, change the number to binary and make sure it has 8 digits. Then, just flip every 0 to a 1 and every 1 to a 0 to get the 1's complement.

🎯 Exam Tip: Always remember to pad the binary number with leading zeros to meet the required bit length (e.g., 8 bits) before inverting the bits for 1's complement calculations.

 

Question 3. Convert \( (46)_{10} \) into a Binary number.
Answer:
To convert a decimal number like 46 to binary, we use repeated division by 2, noting the remainders at each step.
\[ \begin{array}{r|l} 2 & 46 \\ \cline{2-2} 2 & 23 \quad 0 \\ \cline{2-2} 2 & 11 \quad 1 \\ \cline{2-2} 2 & 5 \quad 1 \\ \cline{2-2} 2 & 2 \quad 1 \\ \cline{2-2} 2 & 1 \quad 0 \\ \cline{2-2} & 0 \quad 1 \end{array} \]
Reading the remainders from bottom to top, we get the binary equivalent.
Thus, \( (46)_{10} = (101110)_2 \). The process of converting decimal to binary is essential for computers to understand numbers.
In simple words: To change 46 from our normal counting system to computer binary, you keep dividing 46 by 2 and write down the leftovers. Then, read these leftovers from bottom to top to get the binary number.

🎯 Exam Tip: For decimal to binary conversion, always divide by the base (2) and collect the remainders from bottom to top. Double-check your division and remainder calculations.

 

Question 4. We cannot find 1's complement for \( (28)_{10} \). State reason.
Answer: We cannot find the 1's complement for \( (28)_{10} \) because it is a positive number. The 1's complement is primarily used to represent negative numbers in computer systems, not positive ones. Positive numbers are stored directly in their binary form. This method helps computers perform subtraction using addition.
In simple words: We cannot use 1's complement for \( (28)_{10} \) because it's a positive number. 1's complement is only used for negative numbers in computers.

🎯 Exam Tip: Remember that 1's and 2's complement are methods specifically for representing negative numbers and performing subtraction using addition in binary arithmetic.

 

Question 5. List the encoding systems for characters in memory.
Answer: Computers use several different encoding systems to represent characters in memory. These systems allow computers to store and process text information. Some of the common encoding systems include:

• BCD – Binary Coded Decimal
• EBCDIC – Extended Binary Coded Decimal Interchange Code
• ASCII – American Standard Code for Information Interchange
• Unicode
• ISCII - Indian Standard Code for Information Interchange

Each system has its own way of assigning numerical codes to characters, varying in the number of bits used and the range of characters they can support.
In simple words: There are many ways computers store letters and symbols. Some main ones are BCD, EBCDIC, ASCII, Unicode, and ISCII.

🎯 Exam Tip: List at least three common character encoding systems and briefly mention their purpose to score full marks.

Part III

III. Very Short Answers

 

Question 1. What is radix of a number system? Give example.
Answer: The radix, also known as the base, of a number system uniquely identifies it. It represents the total count of different digits or symbols used in that number system. The radix is the fundamental idea behind how positional number systems work, where the position of a digit gives it a specific value. For example, in the decimal system, the radix is 10 because it uses ten digits (0-9).

In simple words: The radix or base of a number system is how many different digits it uses. For example, the decimal system has a radix of 10 because it uses digits 0 to 9.

🎯 Exam Tip: Clearly define radix as the "count of unique digits" and provide at least two examples with their respective bases.

 

Question 2. Write a note on the binary number system.
Answer: The binary number system is a base-2 system, meaning it uses only two digits: 0 and 1. This system is crucial because computers operate using these two states (on or off). Numbers in the binary system are represented by a sequence of 0s and 1s, and the positional multipliers are powers of 2. For instance, the leftmost bit (Most Significant Bit or MSB) has the largest positional weight, while the rightmost bit (Least Significant Bit or LSB) has the smallest weight.

The number \( 1101_2 \) illustrates this concept:

\( \begin{array}{cccc} 1 & 1 & 0 & 1 \\ \uparrow & \uparrow & \uparrow & \uparrow \\ \text{MSB} & & & \text{LSB} \end{array} \)
In simple words: The binary system uses only 0s and 1s, with a base of 2. The bit on the far left (MSB) has the biggest value, and the bit on the far right (LSB) has the smallest value.

🎯 Exam Tip: When describing the binary system, always mention its base (2), its digits (0 and 1), and the significance of MSB and LSB.

 

Question 3. Convert \( (150)_{10} \) into Binary, then convert that Binary number to Octal.
Answer:
**Decimal to Binary Conversion for 150:**
We use the repeated division by 2 method.
\[ \begin{array}{r|l} 2 & 150 \\ \cline{2-2} 2 & 75 \quad 0 \\ \cline{2-2} 2 & 37 \quad 1 \\ \cline{2-2} 2 & 18 \quad 1 \\ \cline{2-2} 2 & 9 \quad 0 \\ \cline{2-2} 2 & 4 \quad 1 \\ \cline{2-2} 2 & 2 \quad 0 \\ \cline{2-2} 2 & 1 \quad 0 \\ \cline{2-2} & 0 \quad 1 \end{array} \]
Reading remainders from bottom to top, \( (150)_{10} = (10010110)_2 \). This binary number is the machine-readable format for 150.

**Binary to Octal Conversion:**
To convert the binary number \( (10010110)_2 \) to octal, we group the binary digits into sets of three starting from the right. If the leftmost group has fewer than three digits, we add leading zeros.
\( \underbrace{010}_{2} \quad \underbrace{010}_{2} \quad \underbrace{110}_{6} \)
Each group of three binary digits is then converted to its equivalent octal digit.
\( (10010110)_2 = (010 \ 010 \ 110)_2 = (226)_8 \).
So, \( (150)_{10} = (10010110)_2 = (226)_8 \).
In simple words: First, divide 150 by 2 repeatedly and write down the remainders to get the binary number. Then, take this binary number, group its digits in threes from the right, and change each group into its octal digit to get the final octal number.

🎯 Exam Tip: For binary to octal conversion, always group binary digits in threes from the right. Add leading zeros if necessary to complete the leftmost group.

 

Question 4. Write a short note on ISCII.
Answer: ISCII stands for Indian Standard Code for Information Interchange. It is an 8-bit coding system specifically designed to handle characters from Indian local languages, such as Hindi, Tamil, and Malayalam. Because it uses 8 bits, ISCII can represent \( 2^8 = 256 \) different characters. This system was developed by the Department of Electronics in India between 1986 and 1988 and is recognized by the Bureau of Indian Standards (BIS). Today, ISCII is integrated with Unicode, allowing for broader compatibility and use. ISCII helps Indian languages be used in computers.
In simple words: ISCII is a special 8-bit code made in India to help computers use Indian languages. It can show 256 different characters and is now part of Unicode.

🎯 Exam Tip: Highlight that ISCII is an 8-bit system for Indian languages, mentioning its development in India and its integration with Unicode.

 

Question 5. Add : a) \( -22_{10} + 15_{10} \) b) \( 20_{10} + 25_{10} \).
Answer:
a) \( -22_{10} + 15_{10} \)
First, convert 22 and 15 to binary:
22 in binary is \( (10110)_2 \). In 8-bit format, it's \( (00010110)_2 \).
15 in binary is \( (00001111)_2 \).
To represent \( -22_{10} \), we use 2's complement of 22:
1's complement of \( (00010110)_2 \) is \( (11101001)_2 \).
2's complement of \( (00010110)_2 \) is \( (11101001)_2 + 1 = (11101010)_2 \).
Now add \( (-22)_{10} \) (as 2's complement) to \( 15_{10} \):
\( \quad 11101010 \quad (-22_{10}) \)
\( \underline{+ 00001111 \quad (15_{10})} \)
\( \quad 11111001 \quad \)
The result \( (11111001)_2 \) is a negative number because the most significant bit is 1. To find its decimal value, we take the 2's complement of the result:
1's complement of \( (11111001)_2 \) is \( (00000110)_2 \).
2's complement of \( (11111001)_2 \) is \( (00000110)_2 + 1 = (00000111)_2 \).
This binary \( (00000111)_2 \) is equal to \( 7_{10} \). Since the original MSB was 1, the result is \( -7_{10} \). This calculation demonstrates how computers handle signed number arithmetic.

b) \( 20_{10} + 25_{10} \)
First, convert 20 and 25 to binary:
20 in binary is \( (10100)_2 \).
25 in binary is \( (11001)_2 \).
Now add the binary numbers:
\( \quad \quad 10100 \quad (20_{10}) \)
\( \underline{+ \quad 11001 \quad (25_{10})} \)
\( \quad 101101 \quad (45_{10}) \)
In simple words: For part (a), change both numbers to binary. For the negative number, use 2's complement. Then add them like normal binary numbers. For part (b), convert both numbers to binary and simply add them together.

🎯 Exam Tip: When dealing with negative numbers, always convert them to 2's complement before performing addition. Pay close attention to carry bits during binary addition.

Part IV

IV. Detail Answers.

 

Question 1. a) Write the procedure to convert fractional Decimal to Binary.
Answer:
To convert a fractional decimal number to its binary equivalent, we use the method of repeated multiplication by 2. This process focuses on the fractional part of the number.

The steps involved in this method are:
Step 1: Multiply the decimal fraction by 2. Note down the integer part of the result, which will be either 0 or 1. This integer part is a binary digit.
Step 2: Discard the integer part from the previous product. Then, multiply only the remaining fractional part by 2. Repeat this step continuously until the fractional part becomes 0 (terminates) or until the same fraction starts repeating, meaning you have found the repeating pattern. This process collects more binary digits.
Step 3: The collected integer parts (0s and 1s) from each multiplication form the binary equivalent of the decimal fraction. These digits represent the sequence of bits after the decimal point.
Step 4: Write the final binary answer by listing the integer parts obtained from top to bottom. The first integer part obtained is the most significant bit (closest to the binary point), and the last one is the least significant.

Example: Convert \( (0.2)_{10} \) to Binary.
Here, the integer parts are read from top to bottom to form the fractional binary number.
\( 0.2 \times 2 = 0.4 \quad \rightarrow \quad \text{Integer part: 0} \)
\( 0.4 \times 2 = 0.8 \quad \rightarrow \quad \text{Integer part: 0} \)
\( 0.8 \times 2 = 1.6 \quad \rightarrow \quad \text{Integer part: 1} \)
\( 0.6 \times 2 = 1.2 \quad \rightarrow \quad \text{Integer part: 1} \)
\( 0.2 \times 2 = 0.4 \quad \rightarrow \quad \text{Integer part: 0} \)
(The pattern \( 0.4, 0.8, 1.6, 1.2 \) repeats)
So, \( (0.2)_{10} = (0.00110011...)_2 = (0.00110011)_2 \). This method is used when an exact representation is not possible, often leading to a repeating binary fraction.
In simple words: To change a decimal fraction to binary, keep multiplying the fraction by 2. Write down the whole number part (0 or 1) each time. Read these whole numbers from top to bottom to get your binary fraction.

🎯 Exam Tip: When converting fractional decimals to binary, always remember to multiply the fractional part by 2, not the whole number. Stop when the fractional part is zero or a repeating pattern is observed.

 

Question 1. b) Convert \( (98.46)_{10} \) to Binary.
Answer:
To convert \( (98.46)_{10} \) to Binary, we convert the integral part (98) and the fractional part (0.46) separately.

**Conversion of Integral Part (98) to Binary:**
Use repeated division by 2:
\[ \begin{array}{r|l} 2 & 98 \\ \cline{2-2} 2 & 49 \quad 0 \\ \cline{2-2} 2 & 24 \quad 1 \\ \cline{2-2} 2 & 12 \quad 0 \\ \cline{2-2} 2 & 6 \quad 0 \\ \cline{2-2} 2 & 3 \quad 0 \\ \cline{2-2} 2 & 1 \quad 1 \\ \cline{2-2} & 0 \quad 1 \end{array} \]
Reading remainders from bottom to top, \( (98)_{10} = (1100010)_2 \).

**Conversion of Fractional Part (0.46) to Binary:**
Use repeated multiplication by 2:
\( 0.46 \times 2 = 0.92 \quad \rightarrow \quad \text{Integer part: 0} \)
\( 0.92 \times 2 = 1.84 \quad \rightarrow \quad \text{Integer part: 1} \)
\( 0.84 \times 2 = 1.68 \quad \rightarrow \quad \text{Integer part: 1} \)
\( 0.68 \times 2 = 1.36 \quad \rightarrow \quad \text{Integer part: 1} \)
\( 0.36 \times 2 = 0.72 \quad \rightarrow \quad \text{Integer part: 0} \)
\( 0.72 \times 2 = 1.44 \quad \rightarrow \quad \text{Integer part: 1} \)
\( 0.44 \times 2 = 0.88 \quad \rightarrow \quad \text{Integer part: 0} \)
\( 0.88 \times 2 = 1.76 \quad \rightarrow \quad \text{Integer part: 1} \)
... and so on. This part is a repeating fraction. So, \( (0.46)_{10} \approx (0.01110101...)_2 \).

Combining both parts, \( (98.46)_{10} = (1100010.01110101...)_2 \). This process shows how real numbers are approximated in binary by separating their whole and fractional components.
In simple words: First, change the whole number (98) to binary by dividing by 2. Then, change the decimal part (0.46) to binary by multiplying by 2. Put both binary results together with a dot in between.

🎯 Exam Tip: Always convert the integral and fractional parts of a mixed decimal number separately to binary, then combine them using a binary point.

 

Question 2. Find 1's Complement and 2's Complement for the following Decimal number.
a) -98
b) -135
Answer:
a) For \( -98_{10} \):
First, convert the absolute value, 98, to binary:
\[ \begin{array}{r|l} 2 & 98 \\ \cline{2-2} 2 & 49 \quad 0 \\ \cline{2-2} 2 & 24 \quad 1 \\ \cline{2-2} 2 & 12 \quad 0 \\ \cline{2-2} 2 & 6 \quad 0 \\ \cline{2-2} 2 & 3 \quad 0 \\ \cline{2-2} 2 & 1 \quad 1 \\ \cline{2-2} & 0 \quad 1 \end{array} \]
So, \( (98)_{10} = (1100010)_2 \).
In 8-bit format, \( (98)_{10} = (01100010)_2 \).
Now, find 1's complement of \( (01100010)_2 \):
1's complement of \( (-98)_{10} \) = \( (10011101)_2 \).
Then, find 2's complement by adding 1 to 1's complement:
2's complement of \( (-98)_{10} \) = \( (10011101)_2 + 1 = (10011110)_2 \).

b) For \( -135_{10} \):
First, convert the absolute value, 135, to binary:
\[ \begin{array}{r|l} 2 & 135 \\ \cline{2-2} 2 & 67 \quad 1 \\ \cline{2-2} 2 & 33 \quad 1 \\ \cline{2-2} 2 & 16 \quad 1 \\ \cline{2-2} 2 & 8 \quad 0 \\ \cline{2-2} 2 & 4 \quad 0 \\ \cline{2-2} 2 & 2 \quad 0 \\ \cline{2-2} 2 & 1 \quad 0 \\ \cline{2-2} & 0 \quad 1 \end{array} \]
So, \( (135)_{10} = (10000111)_2 \).
In 8-bit format, \( (135)_{10} = (10000111)_2 \).
Now, find 1's complement of \( (10000111)_2 \):
1's complement of \( (-135)_{10} \) = \( (01111000)_2 \).
Then, find 2's complement by adding 1 to 1's complement:
2's complement of \( (-135)_{10} \) = \( (01111000)_2 + 1 = (01111001)_2 \).
These complement forms are how computers manage negative numbers in arithmetic.
In simple words: First, turn the number into binary and make it 8 digits long. For 1's complement, flip all the 0s to 1s and 1s to 0s. For 2's complement, take the 1's complement and then add 1 to it.

🎯 Exam Tip: Always convert the positive equivalent of the decimal number to binary first, ensure it's in the specified bit format (e.g., 8-bit), then apply the 1's complement (bit flip) and 2's complement (add 1).

 

Question 3. a) Add \( 1101010_2 + 101101_2 \)
Answer:
To add binary numbers, we use the same principle as decimal addition, but with only two digits (0 and 1) and specific carry rules. When adding 1 + 1, the result is 0 with a carry of 1. Always align the numbers by their rightmost digit. This addition is basic to all computer calculations.

\( \quad \quad \quad 1 \quad 1 \quad \leftarrow \text{carry to next digit} \)
\( \quad \quad 1101010_2 \)
\( \underline{+ \quad 0101101_2} \)
\( \quad 10010111_2 \)

Thus, \( 1101010_2 + 101101_2 = 10010111_2 \).
In simple words: Add the binary numbers just like regular numbers, but remember that 1 + 1 is 0 and you carry over a 1 to the next spot.

🎯 Exam Tip: When performing binary addition, remember the rules: 0+0=0, 0+1=1, 1+0=1, 1+1=0 (carry 1). Practice aligning numbers correctly, especially if they have different lengths.

 

Question 3. b) Subtract \( 1101011_2 - 111010_2 \).
Answer:
To subtract binary numbers, we often use the borrowing method similar to decimal subtraction. When you need to subtract 1 from 0, you borrow from the next more significant bit. The borrowed 1 becomes \( 10_2 \) (which is 2 in decimal). If the next bit is 0, you borrow from the bit after that, making all intermediate 0s into 1s. Binary subtraction is a fundamental operation in digital circuits. Let's perform the subtraction:

\( \quad \quad \quad 1 \quad 1 \quad \leftarrow \text{Borrow from previous digit} \)
\( \quad \quad 1101011_2 \)
\( \underline{- \quad 0111010_2} \)
\( \quad \quad 0110001_2 \)

Thus, \( 1101011_2 - 111010_2 = 0110001_2 \).
In simple words: To subtract binary numbers, line them up and subtract column by column. If you need to subtract 1 from 0, you "borrow" from the left, turning the 0 into 10 (which is 2).

🎯 Exam Tip: For binary subtraction, correctly handling borrows is critical. A borrow converts a 0 to a \( 10_2 \) (decimal 2) and reduces the digit from which you borrowed.

11th Computer Science Guide Number Systems Additional Questions And Answers

Part I

Choose The Correct Answer.

 

Question 1. The simplest method to represent a negative binary number is called ________.
(b) sign bit or parity bit
(c) binary
(d) decimal
Answer: (a) signed magnitude
In simple words: The easiest way to show a negative number in binary is called "signed magnitude." You use one special bit to show if the number is positive or negative, and the rest of the bits show its actual size.

🎯 Exam Tip: Remember that signed magnitude is the most straightforward but not always the most efficient method for representing negative numbers due to issues like having two representations for zero.

 

Question 2. Computer understand ________ language.
a) High level
b) Assembly
c) Machine
d) All the options
Answer: (c) Machine
In simple words: Computers only understand 'machine language,' which is made up of 0s and 1s. All other languages must be translated into machine language for the computer to follow instructions.

🎯 Exam Tip: Distinguish between high-level languages (like Python, Java), assembly language, and machine language, noting that only machine language is directly executed by the CPU.

 

Question 3. Expansion for BCD ________.
(a) Binary coded decimal
(b) binary complement decimal
(c) binary computer decimal
(d) binary convert decimal
Answer: (a) Binary coded decimal
In simple words: BCD stands for 'Binary Coded Decimal.' It's a way to show decimal numbers where each digit (0-9) is given its own 4-bit binary code.

🎯 Exam Tip: Be precise with acronym expansions. For BCD, ensure you state "Binary Coded Decimal," not variations.

 

Question 4. ________ is the basic unit of data in computer.
a) BIT
b) BYTE
c) NIBBLE
Answer: (a) BIT
In simple words: The smallest piece of information a computer can handle is called a 'bit,' which can be either a 0 or a 1. All other data units are built from bits.

🎯 Exam Tip: Clearly identify the bit as the smallest unit. Understand how other units (nibble, byte, word) are formed from bits.

 

Question 5. The ____________ operator is defined in boolean algebra by the use of the dot (.) operator.
(a) AND
(b) OR
(c) NOT
(d) NAND
Answer: (a) AND
In simple words: In Boolean algebra, the dot (.) symbol is used to represent the AND operation. It combines two inputs, and the output is true only if both inputs are true.

🎯 Exam Tip: Remember that in Boolean algebra, the dot represents AND, a plus (+) represents OR, and an apostrophe (') or bar (¯) represents NOT.

 

Question 6. Binary digit means ____________.
(a) 0
(b) 1
(c) either 0 or 1
(d) None of the options
Answer: (c) either 0 or 1
In simple words: A binary digit, often called a bit, can only be one of two values: 0 or 1. These are the basic building blocks of all computer data.

🎯 Exam Tip: Understand that computers use binary because it's easy to represent two states (on/off, high/low voltage) with electrical signals.

 

Question 7. The convert (65)10 into its equivalent octal number ____________.
(a) \( (101)_8 \)
(b) \( (101)_{10} \)
(c) \( (101)_{12} \)
Answer: (a) \( (101)_8 \)
In simple words: To change a base-10 number like 65 into a base-8 (octal) number, you repeatedly divide 65 by 8 and write down the remainders. The result is 101 in octal.

🎯 Exam Tip: Always remember to collect the remainders from bottom to top when converting from decimal to other bases like octal or binary.

 

Question 8. A collection of 8 bits is called ____________.
(a) BIT
(b) BYTE
(c) NIBBLE
(d) WORD
Answer: (b) BYTE
In simple words: A byte is a group of 8 bits, which is a common unit for measuring computer memory and data size. It's often enough to store one character, like a letter or number.

🎯 Exam Tip: Distinguish between a bit (single 0 or 1), a nibble (4 bits), and a byte (8 bits) as these are fundamental units in computer science.

 

Question 9. ____________ is the general idea behind the positional numbering system.
(a) Radix
(b) Computer memory
(c) Binary number
(d) Decimal number
Answer: (a) Radix
In simple words: Radix, also known as the base, tells us how many unique digits a number system uses. For example, the decimal system has a radix of 10. This value defines the system's ability to represent numbers based on the position of digits.

🎯 Exam Tip: Understand that the radix determines the value each digit holds based on its position, making a positional numbering system work.

 

Question 10. ____________ refers to the number of bits processed by a computer's CPU.
(a) Word length
(b) Nibble
(c) Word size
(d) None of the options
Answer: (a) Word length
In simple words: The word length tells us how many bits a computer's CPU can handle at one time. A bigger word length means the computer can process more data faster.

🎯 Exam Tip: Remember that word length (or word size) is a key feature of a CPU's architecture, affecting its overall performance.

 

Question 11. Bit means ____________.
(a) nibble
(b) byte
(c) word length
(d) binary digit
Answer: (d) binary digit
In simple words: A bit is simply a binary digit, which is the smallest unit of data in a computer, represented as either a 0 or a 1. All digital information is made up of these tiny bits.

🎯 Exam Tip: It is crucial to remember that a bit is the most basic unit, representing a single binary state.

 

Question 12. ____________ is a valid word length of a computer.
(a) 64
(b) 32
(c) 16
(d) All the options
Answer: (d) All the options
In simple words: Word length tells us how many bits a CPU can process at once, and 16, 32, and 64 bits are all common valid word lengths for computers. Modern computers often use 64-bit word lengths.

🎯 Exam Tip: Be aware that computer architectures vary, and different systems can have different word lengths, with larger ones generally indicating more powerful processors.

 

Question 13. The computer can understand ____________ languages.
(a) computer
(b) machine
(c) post
(d) pre
Answer: (b) machine
In simple words: Computers directly understand machine language, which is made up of binary code (0s and 1s). All other programming languages must be translated into machine language for the computer to execute them.

🎯 Exam Tip: Remember that machine language is the lowest-level programming language, directly executed by the CPU.

 

Question 14. 1 KiloByte equals to ____________ bytes.
(a) 1024
(b) 256
(c) 1000
(d) 128
Answer: (a) 1024
In simple words: One Kilobyte (KB) is equal to 1024 bytes, not 1000, because computers use powers of 2 for memory measurements. This is a common unit for small files or memory sizes.

🎯 Exam Tip: Always remember that computer memory units are based on powers of 2, so a kilobyte is \( 2^{10} \) bytes.

 

Question 15. How many bytes does 1 zettabyte contain?
(a) \( 2^{90} \)
(b) \( 2^{80} \)
(c) \( 2^{70} \)
(d) \( 2^{60} \)
Answer: (c) \( 2^{70} \)
In simple words: A zettabyte (ZB) is a very large unit of digital information, equal to \( 2^{70} \) bytes. This is because each unit of computer memory scales by powers of 1024.

🎯 Exam Tip: Memorize the prefixes for data storage (Kilo, Mega, Giga, Tera, Peta, Exa, Zetta, Yotta) and their corresponding powers of 2.

 

Question 16. 1024 MegaBytes equals to ____________.
(a) 1 GigaByte
(b) 1 TeraByte
(c) 1 YottaByte
(d) None of these
Answer: (a) 1 GigaByte
In simple words: Just like 1024 kilobytes make a megabyte, 1024 megabytes (MB) make one gigabyte (GB). This is a standard conversion in computer storage.

🎯 Exam Tip: Remember the basic hierarchy: 1024 Bytes = 1 KB, 1024 KB = 1 MB, 1024 MB = 1 GB, and so on.

 

Question 18. 1-kilo byte represents ____________ bytes.
(a) 512
(b) 256
(c) 1024
(d) 64
Answer: (c) 1024
In simple words: A kilobyte is a unit of digital information storage equal to 1024 bytes. This is a standard conversion based on powers of two in computing.

🎯 Exam Tip: Double-check the common memory unit conversions; a kilobyte is often approximated as 1000 bytes, but in actual computing, it's 1024 bytes.

 

Question 18. 1Kb equals to ____________ bytes.
(a) \( 2^{10} \)
(b) \( 2^{20} \)
(c) \( 2^{30} \)
(d) \( 2^{40} \)
Answer: (a) \( 2^{10} \)
In simple words: In computer science, 1 Kilobyte (KB) is precisely equal to \( 2^{10} \) bytes, which calculates to 1024 bytes. This is why memory is often measured in powers of two.

🎯 Exam Tip: Understand that \( 2^{10} \) is the base for 'kilo' in digital measurements, while 'kilo' in other contexts means 1000.

 

Question 19. How many megabytes does 1 GB contain?
(a) \( 2^{20} \)
(b) \( 2^{10} \)
(c) \( 2^{30} \)
(d) \( 2^{40} \)
Answer: (b) \( 2^{10} \)
In simple words: A Gigabyte (GB) contains \( 2^{10} \) Megabytes (MB), which is 1024 MB. This represents a larger unit in the hierarchy of computer memory.

🎯 Exam Tip: Recall that each step up in memory units (KB to MB, MB to GB, etc.) typically involves a multiplication by 1024, or \( 2^{10} \).

 

Question 20. 1 GB equals to ____________ bytes.
(a) \( 2^{10} \)
(b) \( 2^{20} \)
(c) \( 2^{30} \)
(d) \( 2^{40} \)
Answer: (c) \( 2^{30} \)
In simple words: One Gigabyte (GB) is equal to \( 2^{30} \) bytes, which is a very large number of bytes. This unit is commonly used to measure the storage capacity of hard drives and large files.

🎯 Exam Tip: Practice converting between bytes, kilobytes, megabytes, and gigabytes using powers of 2 for quick calculations.

 

Question 21. What is the 1' s complement of 11001?
(a) 11100110
(b) 01010101
(c) 11110000
(d) 100100111
Answer: (a) 11100110
In simple words: To find the 1's complement of a binary number, you flip each digit: change all 0s to 1s and all 1s to 0s. Assuming 11001 is part of an 8-bit number (00011001), its 1's complement would be 11100110.

🎯 Exam Tip: When finding complements, always be aware of the specified number of bits (e.g., 8-bit, 16-bit) as it affects leading zeros and the final result.

 

Question 22. 1 PetaByte(PB) equals to ____________ bytes.
(a) \( 2^{50} \)
(b) \( 2^{60} \)
(c) \( 2^{70} \)
(d) \( 2^{80} \)
Answer: (a) \( 2^{50} \)
In simple words: A Petabyte (PB) is a massive unit of digital storage, equivalent to \( 2^{50} \) bytes. This unit is used for extremely large data sets, such as those found in big data analysis or cloud storage.

🎯 Exam Tip: Practice recognizing the power-of-2 equivalents for Peta, Exa, Zetta, and Yotta bytes as these are commonly tested for large storage units.

 

Question 23. The hexadecimal equivalent of 15 is ____________.
(a) A
(b) B
(c) E
(d) F
Answer: (d) F
In simple words: In the hexadecimal number system, which uses base 16, numbers from 10 to 15 are represented by letters A to F. So, the decimal number 15 is represented as F in hexadecimal.

🎯 Exam Tip: Memorize the hexadecimal digits: 0-9 and A (10), B (11), C (12), D (13), E (14), F (15).

 

Question 25. The radix of a hexadecimal number is ____________.
(a) 2
(b) 8
(c) 16
(d) 10
Answer: (c) 16
In simple words: The radix, or base, of a number system tells you how many different digits it uses. For hexadecimal, it uses 16 unique symbols (0-9 and A-F).

🎯 Exam Tip: Clearly understand that binary has a radix of 2, octal 8, decimal 10, and hexadecimal 16.

 

Question 26. Computer memory is normally represented in terms of ____________ bytes.
(a) Kilo
(b) Mega
(c) Kilo or Mega
(d) None of these
Answer: (c) Kilo or Mega
In simple words: Computer memory is often measured in kilobytes (KB) for smaller amounts or megabytes (MB) for larger amounts. These units help describe the capacity of RAM or storage.

🎯 Exam Tip: While gigabytes and terabytes are also common, Kilo and Mega are foundational units for representing memory sizes.

 

Question 27. The most commonly used number system is ____________.
(a) binary
(b) decimal
(c) octal
(d) hexadecimal
Answer: (b) decimal
In simple words: The decimal number system, which uses ten digits (0-9), is the system most people use every day in real life. Computers, however, operate using the binary system.

🎯 Exam Tip: Distinguish between the decimal system (human use) and the binary system (computer use) as they are based on different bases.

 

Question 28. The most commonly used coding scheme to represent character set and the number is ____________.
(a) BCD
(b) ASCII
(c) EBCDIC
(d) All the options
Answer: (b) ASCII
In simple words: ASCII (American Standard Code for Information Interchange) is a widely used coding system for representing text characters in computers. It assigns unique numbers to letters, numbers, and symbols.

🎯 Exam Tip: Remember ASCII is fundamental for text representation, though Unicode has largely superseded it for supporting a broader range of languages.

 

Question 29. What does MSB mean?
(a) Major sign bit
(b) Most sign bit
(c) Minor sign bit
(d) Most significant bit
Answer: (d) Most significant bit
In simple words: MSB stands for Most Significant Bit, which is the bit in a binary number that has the greatest value. It is always the leftmost bit.

🎯 Exam Tip: Understand that MSB determines the largest part of a number's value, while LSB (Least Significant Bit) determines the smallest part.

 

Question 30. The ASCII value for blank space is ____________.
(a) 43
(b) 42
(c) 32
Answer: (c) 32
In simple words: In the ASCII character encoding system, the number 32 is assigned to represent a blank space. This allows computers to store and display spaces correctly in text.

🎯 Exam Tip: Familiarize yourself with common ASCII values for important characters like space, 'A', 'a', '0' as they frequently appear in questions.

 

Question 31. The binary equivalent of hexadecimal number B is ____________.
(a) 1011
(b) 1100
(c) 1001
(d) 1010
Answer: (a) 1011
In simple words: The hexadecimal digit B represents the decimal number 11. To convert this to binary, we find the 4-bit binary code for 11, which is 1011.

🎯 Exam Tip: Remember that each hexadecimal digit can be directly translated into a 4-bit binary number, which simplifies conversions.

 

Question 32. The most commonly used numbering system in real life is the ____________ number system.
(a) Hexadecimal
(b) Octal
(c) Binary
(d) Decimal
Answer: (d) Decimal
In simple words: The decimal number system, or base-10 system, is what we use every day for counting, calculations, and financial transactions. It is the most familiar system to humans.

🎯 Exam Tip: Always remember that "real life" context usually points to the decimal system, while "computer" context points to binary.

 

Question 33. What is the range of ASCII values for lower case alphabets?
(a) 65 to 90
(b) 65 to 122
(c) 97 to 122
Answer: (c) 97 to 122
In simple words: In the ASCII encoding standard, lowercase letters from 'a' to 'z' are assigned decimal values ranging from 97 to 122. This sequential assignment makes it easy to work with alphabetic characters programmatically.

🎯 Exam Tip: Keep in mind that uppercase letters ('A' to 'Z') have different ASCII values (65-90) than lowercase letters.

 

Question 34. ____________ is the count of number of digits in each number system.
(a) base
(b) radix
(c) base or radix
(d) symbols
Answer: (c) base or radix
In simple words: The base, or radix, of a number system tells us how many unique digits or symbols it uses. For example, the decimal system has a base of 10. This value defines the system's ability to represent numbers based on the position of digits.

🎯 Exam Tip: These terms are often used interchangeably; knowing both "base" and "radix" is important for describing number systems.

 

Question 35. What is the ASCII value for blank space?
(a) 8
(b) 2
(c) 18
(d) 32
Answer: (d) 32
In simple words: The ASCII standard uses the decimal number 32 to represent a single space character. This allows computers to consistently handle spacing in text.

🎯 Exam Tip: Remembering key ASCII values, like 32 for space, 65 for 'A', and 97 for 'a', is helpful for quick recall.

 

Question 36. Identify the true statement from the following.
(a) In the positional number system, each decimal digit is weighted relative to its position in the number.
(b) A numbering system is a way of representing numbers.
(c) The speed of a computer depends on the number of bits it can process at
(d) All the options
Answer: (d) All the options
In simple words: All three statements are correct: positional systems give value based on digit place, numbering systems represent quantities, and CPU speed is linked to how many bits it processes at once. These are fundamental truths about computers and numbers.

🎯 Exam Tip: When faced with "All the above" options, carefully evaluate each statement for its correctness to confirm the best answer.

 

Question 37. Which one of the following bits has the smallest positional weight?
(a) MSB
(b) LSB
(c) UPS
(d) USB
Answer: (b) LSB
In simple words: LSB stands for Least Significant Bit, which is the bit in a binary number that holds the smallest value. It is always the rightmost bit.

🎯 Exam Tip: Understand that the LSB contributes the least to the overall value of a binary number and is often used for parity checks or carrying out arithmetic operations.

 

Question 38. The rightmost bit in the binary number is called as the ____________.
(a) MSB
(b) LSB
(c) FSB
(d) None of these
Answer: (b) LSB
In simple words: The Least Significant Bit (LSB) is the bit at the far right end of a binary number. It has the smallest positional value and changes most frequently during calculations.

🎯 Exam Tip: Remember that LSB is crucial in operations like addition and subtraction, as it's the starting point for carrying and borrowing.

 

Question 39. Name the person who proposed the basic principles of Boolean Algebra?
(a) Wiliam Boole
(b) George Boole
(c) James Boole
(d) Boolean George
Answer: (b) George Boole
In simple words: George Boole was an English mathematician who created Boolean algebra. His work laid the foundation for digital circuit design and modern computer logic.

🎯 Exam Tip: It is important to know the key figures in computer science history, like George Boole, for their foundational contributions.

 

Question 40. ____________ numbers are used as a shorthand form of a binary sequence.
(a) Hexadecimal
(b) Octal
(c) Decimal
(d) None of these
Answer: (a) Hexadecimal
In simple words: Hexadecimal numbers are often used to make long binary sequences shorter and easier to read. Since each hexadecimal digit represents four binary bits, it's a very compact way to write binary data.

🎯 Exam Tip: Understand that hexadecimal is frequently used in programming and memory addressing because it efficiently represents binary data.

 

Question 41. What is the other name for a logical statement?
(a) Truth values
(b) Truth functions
(c) Truth table
(d) Truth variables
Answer: (b) Truth functions
In simple words: A logical statement can also be called a truth function because its output (true or false) depends on the truth values of its inputs. This concept is central to Boolean logic.

🎯 Exam Tip: Remember that logical statements evaluate to either true or false, forming the basis of decision-making in computer programs.

 

Question 42. In hexadecimal number system letter 'E' represents ____________.
(a) 12
(b) 13
(c) 14
(d) 15
Answer: (c) 14
In simple words: In hexadecimal, the letter E stands for the decimal number 14. This is part of the system where letters A through F are used to represent values from 10 to 15.

🎯 Exam Tip: Practice converting decimal numbers 10-15 to their hexadecimal letter equivalents (A-F) to avoid confusion.

 

Question 44. ____________ is a method to convert decimal number to binary number.
(a) Repeated division by 2
(b) Sum of powers of 2
(c) Repeated addition by 2
(d) Either A or B
Answer: (d) Either A or B
In simple words: You can change a decimal number into binary using two main methods: repeatedly dividing by 2 and writing down the remainders, or finding which powers of 2 add up to the decimal number. Both methods work well.

🎯 Exam Tip: Be comfortable with both conversion methods, as some questions might ask for a specific method, or one might be easier for certain numbers.

 

Question 45. The output for the AND operator is ____________.
(a) A + B
(b)
(c) A.B
(d) AB + C
Answer: (c) A.B
In simple words: The AND operator produces a true output only when all of its inputs are true. In Boolean algebra, this operation is written with a dot (.), so 'A AND B' becomes A.B.

🎯 Exam Tip: Clearly understand the symbols for basic Boolean operations: dot for AND, plus for OR, and a bar for NOT.

 

Question 47. Which gate takes only one input?
(a) OR
(b) AND
(c) NOT
(d) XOR
Answer: (c) NOT
In simple words: The NOT gate is unique because it only takes one input and gives the opposite output. For example, if the input is true, the output is false.

🎯 Exam Tip: Identify NOT gates by their single input and their function as an inverter of the input signal.

 

Question 48. In the signed magnitude method, the leftmost bit is called ____________ bit.
(a) sign
(b) parity
(c) sign or parity
(d) None of these
Answer: (c) sign or parity
In simple words: In the signed magnitude method for representing numbers, the very first bit on the left is used to show if the number is positive or negative, and sometimes it can also act as a parity bit to check for errors.

🎯 Exam Tip: Remember that in signed magnitude, a '0' in the leftmost bit means positive, and a '1' means negative, while the rest of the bits represent the number's actual value.

 

Question 49. Which is not a derived date?
(a) AND
(b) NAND
(c) NOR
(d) XOR
Answer: (a) AND
In simple words: The AND gate is a basic logic gate. NAND, NOR, and XOR gates are called derived gates because they are built by combining basic gates like AND, OR, and NOT.

🎯 Exam Tip: Understand the difference between basic logic gates (AND, OR, NOT) and universal gates (NAND, NOR) and derived gates (XOR, XNOR) for circuit design.

Question 50. The numbers are represented in computers in ___method.
(a) Signed magnitude representation
(b) 1's complement
(c) 2's complement
(d) All of the options
Answer: (d) All of the options
In simple words: Computers can store negative numbers using several methods like signed magnitude, 1's complement, and 2's complement. Each method has its own way of showing positive and negative values.

🎯 Exam Tip: Remember that different representation methods are used depending on the type of number being stored and the computational efficiency required.

 

Question 51. The statement "C equal the complement of A or B" means
(a) \( C = \overline{A + B} \)
(b) \( C = \overline{A} + \overline{B} \)
(c) \( C = \overline{A} + \overline{B} \)
(d) \( C = \overline{A \cdot B} \)
Answer: (a) \( C = \overline{A + B} \)
In simple words: When you see "complement of A or B," it means you first combine A and B using "OR" (which is like adding), and then you take the complement of that whole result. The line over the entire expression indicates the complement.

🎯 Exam Tip: Always pay attention to the grouping and order of operations in Boolean algebra, especially when complements are involved, to avoid mistakes like applying complement individually before the 'OR' operation.

 

Question 52. If the number has_sign, it will be considered as negative in signed magnitude representation.
(a) +
(b) no
(c) –
(d) A or B
Answer: (c) –
In simple words: In the signed magnitude system, a negative sign in front of a number tells the computer that it is a negative value. A plus sign or no sign means it's a positive number.

🎯 Exam Tip: In signed magnitude, the leftmost bit is the sign bit (0 for positive, 1 for negative), and the remaining bits represent the magnitude of the number.

 

Question 54. What is the output of the XOR gate?
(a) \( C = A\% B \)
(b) \( C = A \land A \)
(c) \( C = A \odot B \)
(d) \( C = A \oplus B \)
Answer: (d) \( C = A \oplus B \)
In simple words: The XOR gate gives a "true" (1) output only when its inputs are different. The symbol \( \oplus \) is used to show this operation in logic expressions.

🎯 Exam Tip: Remember that the XOR output is 1 if inputs are different (0,1 or 1,0) and 0 if inputs are the same (0,0 or 1,1).

 

Question 54. 2's complement of (00011000)2 is ___
(a) 11100111
(b) 00011001
(c) 11101000
(d) None of the options
Answer: (c) 11101000
In simple words: To find the 2's complement, you first flip all the bits (change 0s to 1s and 1s to 0s) and then add 1 to the result. This helps computers represent negative numbers.

🎯 Exam Tip: Always remember the two steps for 2's complement: 1's complement (flipping bits) followed by adding 1 to the LSB (Least Significant Bit).

 

Question 55. Find \( A + \overline{A} \cdot B \) = ___
(a) \( A + B \)
(b) \( A \cdot B \)
(c) \( \overline{A \cdot B} \)
(d) \( \overline{A \cdot B} \)
Answer: (a) \( A + B \)
In simple words: This is a rule in Boolean algebra called the absorption law, which simplifies the expression. It means "A OR (NOT A AND B)" is the same as "A OR B".

🎯 Exam Tip: Recognize and apply Boolean algebra identities like the absorption law (A + A'B = A + B) to simplify expressions efficiently.

 

Question 56. When two binary numbers are added ___ will be the output.
(a) sum
(b) carry
(c) sum and carry
(d) None of the options
Answer: (c) sum and carry
In simple words: When you add two binary numbers, just like regular numbers, you get a sum for each position and sometimes a "carry" digit that goes over to the next position. This process forms the basis of binary arithmetic.

🎯 Exam Tip: Remember the basic binary addition rules: 0+0=0 (sum 0, carry 0), 0+1=1 (sum 1, carry 0), 1+0=1 (sum 1, carry 0), 1+1=10 (sum 0, carry 1).

 

Question 57. When subtracting 1 from 0, borrow 1 from the next ___
(a) LSB
(b) MSB
(c) either A or B
(d) None of the options
Answer: (b) MSB
In simple words: In binary subtraction, when you need to subtract 1 from 0, you have to "borrow" from the next bit to the left, which is usually the Most Significant Bit (MSB) if no intermediate bits can provide a borrow. This is similar to borrowing in decimal subtraction.

🎯 Exam Tip: Understand that borrowing in binary subtraction propagates from left to right, affecting bits with higher positional values first.

 

Question 58. Find the wrong pair from the following:
(a) Null element: \( A + 1 = 1 \)
(b) Involution: \( \overline{\overline{A}} = A \)
(c) Demorgan's: \( \overline{A + B} = \overline{A} \cdot \overline{B} \)
(d) Commutative: \( A + B = B \cdot A \)
Answer: (d) Commutative: \( A + B = B \cdot A \)
In simple words: The commutative law in Boolean algebra says that \( A + B \) is the same as \( B + A \) (for OR operation) and \( A \cdot B \) is the same as \( B \cdot A \) (for AND operation). The given option mixes these, making it incorrect.

🎯 Exam Tip: Clearly differentiate between the commutative law for addition (OR) and multiplication (AND) in Boolean algebra: \( A+B = B+A \) and \( A \cdot B = B \cdot A \).

 

Question 59. ___ is the character encoding system.
(a) BCD and ISCII
(b) EBCDIC
(c) BCD
(d) All of the options
Answer: (d) All of the options
In simple words: BCD, EBCDIC, and ISCII are all different ways that computers use to turn characters (like letters and numbers) into binary code. They are like different secret languages computers use to understand what we type.

🎯 Exam Tip: Remember that character encoding systems map characters to numeric values, enabling computers to store and process text. Common systems include ASCII, EBCDIC, Unicode, and ISCII.

 

Question 60. With 2 inputs in the truth table, how many sets of values will be obtained.
(a) 4
(b) 8
(c) 2
(d) 1
Answer: (a) 4
In simple words: For a truth table, if you have 2 inputs, each input can be either 0 or 1. This gives \( 2 \times 2 = 4 \) possible combinations of input values, which means 4 rows in the truth table.

🎯 Exam Tip: The number of rows in a truth table for \( n \) inputs is always \( 2^n \).

 

Question 61. EBCDIC stands for ___
(a) Extensive Binary Coded Decimal Interchange Code
(b) Extended Binary Coded Decimal Interchange Code
(c) Extended Binary Coded Digit Interchange Code
(d) Extended Bit Coded Decimal Interchange Code
Answer: (b) Extended Binary Coded Decimal Interchange Code
In simple words: EBCDIC is a special code used by computers, especially older IBM ones, to represent characters like letters and numbers. It's like a language only these computers understand.

🎯 Exam Tip: EBCDIC is an 8-bit character encoding, primarily used on IBM mainframe operating systems, distinguishing it from ASCII which is more common on personal computers.

 

Question 62. ASCII stands for ___
(a) Arithmetic Standard Code for Information Interchange
(b) American Structured Code for Information Interchange
(c) American Standard Code for Information Interchange
(d) American Standard Code for Instant Interchange
Answer: (c) American Standard Code for Information Interchange
In simple words: ASCII is a very common way that computers represent text. It gives a unique number to each letter, number, and symbol so computers can store and share text easily.

🎯 Exam Tip: ASCII is a 7-bit character encoding standard, commonly used for representing text in computers, with each character assigned a unique integer value.

 

Question 63. ISCII stands for ___
(a) International Standard Code for Information Interchange
(b) Indian Structured Code for Information Interchange
(c) India's Standard Code for Information Interchange
(d) Indian Standard Code for Information Interchange
Answer: (d) Indian Standard Code for Information Interchange
In simple words: ISCII is a special coding system used in computers to handle local Indian languages. It helps computers display and process text in languages like Hindi, Tamil, and many others.

🎯 Exam Tip: ISCII is an 8-bit encoding developed by the Bureau of Indian Standards (BIS) to support Indian scripts alongside Latin characters.

 

Question 64. BCD is ___ bit code.
(a) 6
(b) 7
(c) 8
(d) None of the options
Answer: (a) 6
In simple words: BCD stands for Binary Coded Decimal. It is a way to encode decimal numbers, and traditionally, it uses 6 bits to represent each character.

🎯 Exam Tip: While some BCD variations exist, the standard BCD used for encoding characters often refers to a 6-bit system allowing 64 possible characters.

 

Question 65. EBCDIC is ___ bit code.
(a) 6
(b) 7
(c) 8
(d) None of the options
Answer: (c) 8
In simple words: EBCDIC is a character coding system that uses 8 bits for each character. This means it can represent many more characters than a 6-bit system.

🎯 Exam Tip: An 8-bit code like EBCDIC can represent \( 2^8 = 256 \) different characters, which is useful for supporting a wider range of symbols.

 

Question 66. ASCII is ___ bit code
(a) 6
(b) 7
(c) 8
(d) None of the options
Answer: (b) 7
In simple words: ASCII is a character coding system that uses 7 bits for each character. This means it can represent \( 2^7 \), or 128, different characters.

🎯 Exam Tip: While ASCII is fundamentally 7-bit, it is often extended to 8 bits (e.g., ASCII-8 or Extended ASCII) to support additional characters, but the core standard is 7-bit.

 

Question 67. Unicode is ___ bit code
(a) 16
(b) 7
(c) 8
(d) None of the options
Answer: (a) 16
In simple words: Unicode is a very large character encoding system that uses 16 bits (and more) per character. This allows it to represent almost all written languages in the world.

🎯 Exam Tip: Unicode was developed to overcome the limitations of older encoding systems like ASCII and EBCDIC, supporting a vast range of characters across multiple languages globally.

 

Question 68. ISCII is ___ bit code
(a) 16
(b) 7
(c) 8
(d) None of the options
Answer: (c) 8
In simple words: ISCII is a character encoding system that uses 8 bits for each character. This allows it to handle characters from Indian languages along with English.

🎯 Exam Tip: As an 8-bit code, ISCII can represent up to 256 characters, making it suitable for bilingual computing (English and Indian scripts).

 

Question 69. ___ coding system is formulated by IBM.
(a) BCD
(b) EBCDIC
(c) BCD
(d) None of the options
Answer: (b) EBCDIC
In simple words: EBCDIC is a character coding system that was created by IBM. It is primarily used in their mainframe computers.

🎯 Exam Tip: Remember that EBCDIC is closely associated with IBM's proprietary systems, unlike ASCII which gained widespread adoption across various platforms.

 

Question 70. IBM stands for ___
(a) Indian Business Machine
(b) International Basic Machine
(c) International Business Method
(d) International Business Machine
Answer: (d) International Business Machine
In simple words: IBM is a well-known company in the field of technology and its name stands for "International Business Machine." It develops and sells computer hardware, software, and services.

🎯 Exam Tip: Knowing common technology acronyms like IBM can help in understanding the history and key players in computer science.

 

Question 71. ___ is the system of handling the characters of Indian local languages.
(a) ASCII
(b) Unicode
(c) BCD
(d) ISCII
Answer: (d) ISCII
In simple words: ISCII is the specific system made to help computers work with and show characters from different local languages spoken in India.

🎯 Exam Tip: ISCII's primary function is to enable computing in Indian languages, highlighting the need for specialized encoding beyond universal systems for regional scripts.

 

Question 72. ISCII system is formulated by the ___ in India.
(a) Department of Electronics
(b) Department of Electricity
(c) Department of E-commerce
(d) Department of Economics
Answer: (a) Department of Electronics
In simple words: The ISCII system, which helps computers with Indian languages, was created by the Department of Electronics in India. This shows how important it was to have a standard for Indian language computing.

🎯 Exam Tip: Remember the specific body (Department of Electronics) responsible for developing ISCII to accurately answer questions about its origin.

 

Question 73. SCO system can handle ___ characters.
(a) 64
(b) 128
(c) 256
(d) 65536
Answer: (a) 64
In simple words: The SCO system is an older type of computer character code, and it can work with 64 different characters. This is a smaller number compared to newer systems.

🎯 Exam Tip: Recognize that older encoding systems like SCO had limited character sets due to fewer bits used per character.

 

Question 74. EBCDIC system can handle ___ characters.
(a) 64
(b) 128
(c) 256
(d) None of the options
Answer: (c) 256
In simple words: The EBCDIC system uses 8 bits for each character, which means it can represent \( 2^8 \), or 256, different characters. This makes it useful for systems that need more symbols than older 6-bit codes.

🎯 Exam Tip: Relate the number of bits in an encoding system directly to the total number of characters it can represent (\( 2^{\text{number of bits}} \)).

 

Question 75. ASCII system can handle ___ characters.
(a) 64
(b) 128
(c) 256
(d) None of the options
Answer: (c) 256
In simple words: While standard ASCII handles 128 characters, the extended ASCII system uses 8 bits, allowing it to handle \( 2^8 \), or 256, different characters. This includes the basic ASCII set plus additional symbols.

🎯 Exam Tip: Differentiate between standard 7-bit ASCII (128 characters) and 8-bit extended ASCII (256 characters) when answering questions about character capacity.

 

Question 77. ISCII system can handle ___ characters.
(a) 64
(b) 128
(c) 256
(d) 65535
Answer: (c) 256
In simple words: The ISCII system, which helps computers display Indian languages, is an 8-bit code. This means it can represent \( 2^8 \), or 256, unique characters, allowing for a good range of linguistic support.

🎯 Exam Tip: Remember that ISCII's 8-bit structure allows it to accommodate both Latin characters and a comprehensive set of Indian script characters.

 

Question 78. ___ language characters are not represented by ASCII.
(a) Tamil
(b) Malayalam
(c) Telugu and Kannada
(d) All of the options
Answer: (d) All of the options
In simple words: Standard ASCII is a basic code mainly for English characters and symbols. It cannot represent the complex characters found in Indian languages like Tamil, Malayalam, Telugu, and Kannada, which require more advanced encoding systems.

🎯 Exam Tip: ASCII's 7-bit or 8-bit capacity is insufficient for many non-Latin script languages, necessitating encodings like Unicode or ISCII for broader linguistic support.

 

Question 79. Tamil, Malayalam, Telugu, and Kannada language characters are represented by ___ code.
(a) ASCII
(b) EBCDIC
(c) BCD
(d) All of the options
Answer: (d) All of the options
In simple words: Indian languages like Tamil, Malayalam, Telugu, and Kannada are represented using special character codes such as ISCII and Unicode. These codes have enough space to handle all the unique letters and symbols of these languages.

🎯 Exam Tip: While ISCII is specifically for Indian languages, Unicode provides universal support for all global languages, including these Indian scripts.

 

Question 80. ___ scheme is denoted by hexadecimal numbers
(a) ASCII
(b) Unicode
(c) BCD
(d) ISCII
Answer: (b) Unicode
In simple words: Unicode is a comprehensive coding system that assigns a unique number to almost every character in every language. These numbers are often written and represented using hexadecimal digits.

🎯 Exam Tip: Hexadecimal notation is commonly used to represent Unicode code points because it offers a compact and human-readable way to express the large range of values.

 

Question 81. ISCII code was formulated in the year ___
(a) 1986-88
(b) 1984-86
(c) 1988-90
(d) 1987
Answer: (a) 1986-88
In simple words: The ISCII character coding system, designed for Indian languages, was created and finalized during the years 1986 to 1988. This was a key step in bringing Indian language computing forward.

🎯 Exam Tip: Knowing the development timeline for key encoding standards helps understand their historical context and evolution.

 

Question 82. ___ coding system is integrated with Unicode.
(a) ASCII
(b) EBCDIC
(c) BCD
(d) ISCII
Answer: (d) ISCII
In simple words: The ISCII coding system, which handles Indian languages, has been combined with Unicode. This means that Unicode can now also properly display and work with characters from ISCII.

🎯 Exam Tip: Integration with Unicode ensures that national standards like ISCII can be supported within a global character encoding framework, promoting wider compatibility.

 

Question 83. ___ was generated to handle all the coding system of Universal languages.
(a) ASCII
(b) Unicode
(c) BCD
(d) ISCII
Answer: (b) Unicode
In simple words: Unicode was created to be a single, universal coding system that could represent characters from every language in the world. It solves the problem of different languages needing different codes.

🎯 Exam Tip: Unicode's primary goal is universal character encoding, enabling seamless exchange and display of text across all languages and platforms.

 

Question 84. The popular coding scheme after ASCII is ___
(a) EBCDIC
(b) Unicode
(c) BCD
(d) ISCII
Answer: (b) Unicode
In simple words: After ASCII became widely used, Unicode emerged as the next popular coding system. It was designed to support many more characters and languages than ASCII could.

🎯 Exam Tip: Unicode addressed the limitations of ASCII, particularly its inability to support diverse international languages, making it the de facto standard for modern text representation.

 

Question 85. BCD system is ___ bit encoding system.
(a) \( 2^8 \)
(b) \( 2^{16} \)
(c) \( 2^6 \)
(d) \( 2^4 \)
Answer: (c) \( 2^6 \)
In simple words: The BCD system, used for encoding decimal numbers, typically works with 6 bits. This means it can represent 64 different characters or values.

🎯 Exam Tip: Remember that a 6-bit system can represent \( 2^6 = 64 \) unique characters, which defines its character set capacity.

 

Question 86. EBCDIC system is ___ bit encoding system.
(a) \( 2^8 \)
(b) \( 2^{16} \)
(c) \( 2^6 \)
(d) \( 2^7 \)
Answer: (a) \( 2^8 \)
In simple words: The EBCDIC system, mainly used by IBM, is an 8-bit encoding system. This means it can represent \( 2^8 \), or 256, different characters.

🎯 Exam Tip: Clearly link the \( 2^n \) notation to the number of characters an \( n \)-bit encoding system can represent.

 

Question 87. ASCII system is a bit encoding system.
(a) \( 2^8 \)
(b) \( 2^{16} \)
(c) \( 2^6 \)
(d) \( 2^7 \)
Answer: (d) \( 2^7 \)
In simple words: The standard ASCII system uses 7 bits for encoding. This means it can represent \( 2^7 \), or 128, distinct characters. This is often expanded for more characters.

🎯 Exam Tip: Understand that the number of distinct characters an encoding system can represent is given by \( 2^{\text{number of bits}} \).

 

Question 88. Unicode system is ___ bit encoding system.
(a) \( 2^8 \)
(b) \( 2^{16} \)
(c) \( 2^6 \)
(d) \( 2^7 \)
Answer: (b) \( 2^{16} \)
In simple words: The Unicode system commonly uses 16 bits for encoding characters. This allows it to represent \( 2^{16} \), or 65,536, different characters, covering almost all global languages.

🎯 Exam Tip: Recognize that Unicode's strength lies in its extensive character set, achieved through a larger number of bits per character than older systems.

 

Question 89. ISCII system is ___ bit encoding system.
(a) \( 2^8 \)
(b) \( 2^{16} \)
(c) \( 2^6 \)
(d) \( 2^7 \)
Answer: (b) \( 2^{16} \)
In simple words: The ISCII system uses 8 bits for encoding, but when integrated with Unicode, it often uses a larger bit structure to ensure compatibility across a wider range of characters. In some contexts, it can be seen as part of a 16-bit scheme for broader language support.

🎯 Exam Tip: While ISCII itself is 8-bit, its integration into Unicode often means it benefits from Unicode's larger bit structure for universal representation.

 

Question 90. The input code in ASCII can be converted into ___ system.
(a) EBCDIC
(b) Unicode
(c) BCD
(d) ISCII
Answer: (a) EBCDIC
In simple words: It is possible to change text from ASCII code into EBCDIC code. This conversion is needed when data moves between different types of computer systems, like from a personal computer to an IBM mainframe.

🎯 Exam Tip: Data conversion between ASCII and EBCDIC is a common requirement in environments where both types of systems interact, ensuring character data is correctly interpreted.

 

Question 91. What is ASCII value for 'A' in a decimal number?
(a) 97
(b) 65
(c) 98
(d) 32
Answer: (b) 65
In simple words: In the ASCII system, the uppercase letter 'A' is represented by the decimal number 65. Each character has a specific number that computers use.

🎯 Exam Tip: Memorize the ASCII values for common characters like 'A' (65), 'a' (97), and space (32) as they are frequently tested.

 

Question 92. What is the ASCII value for 'A' in a binary number?
(a) 01100001
(b) 01000001
(c) 01000000
(d) 00100000
Answer: (b) 01000001
In simple words: Since the decimal ASCII value for 'A' is 65, its binary equivalent is 01000001. Computers use these binary codes to store and process text.

🎯 Exam Tip: Practice converting decimal numbers to their 7-bit or 8-bit binary equivalents to quickly find ASCII binary values.

 

Question 93. What is the ASCII value for 'A' in an octal number?
(a) 141
(b) 101
(c) 142
(d) 40
Answer: (b) 101
In simple words: The ASCII decimal value for 'A' is 65. When you convert 65 to octal, you get 101. This is another way computers can represent character codes.

🎯 Exam Tip: To convert decimal 65 to octal, repeatedly divide by 8: \( 65 \div 8 = 8 \) remainder \( 1 \), then \( 8 \div 8 = 1 \) remainder \( 0 \), then \( 1 \div 8 = 0 \) remainder \( 1 \). Reading remainders upwards gives 101.

 

Question 94. What is the ASCII value for 'A' in hexadecimal numbers?
(a) 61
(b) 41
(c) 62
(d) 20
Answer: (b) 41
In simple words: The ASCII decimal value for 'A' is 65. When you convert 65 to hexadecimal, you get 41. Hexadecimal is often used to show binary data in a shorter way.

🎯 Exam Tip: To convert decimal 65 to hexadecimal, divide by 16: \( 65 \div 16 = 4 \) remainder \( 1 \). Reading remainders gives 41.

 

Question 95. Find the false statement in the following.
(a) Computers can handle positive and negative numbers.
(b) MSB is called a sign bit
(c) LSB is called a parity bit
(d) All of the options
Answer: (c) LSB is called a parity bit
In simple words: The Least Significant Bit (LSB) is the rightmost bit in a binary number, representing the smallest value. A parity bit is an extra bit used for error checking, not typically the LSB. So, saying LSB is a parity bit is incorrect.

🎯 Exam Tip: Remember that MSB (Most Significant Bit) often indicates the sign of a number, while a parity bit is an additional bit used for error detection during data transmission.

 

Question 96. Match the following.
a) 78 - (1) Binary number
b) linn - (2) Octal number
c) CAFE - (3) Decimal number
d) 71 - (4) Hexadecimal number
(a) 3, 1, 4, 2
(b) 4, 3, 2, 1
(c) 1, 3, 2, 4
(d) 3, 1, 2, 4
Answer: (a) 3, 1, 4, 2
In simple words: To match, remember that 78 is a decimal number, "linn" is a binary code, "CAFE" is a hexadecimal number, and 71 can be an octal number. We pair each item with its correct number system type.

🎯 Exam Tip: Always identify the base or characteristic of each number or code to match it correctly with its number system. Common bases are 2 (binary), 8 (octal), 10 (decimal), and 16 (hexadecimal).

 

Question 97. In signed magnitude representation, ____ in the sign bit represents negative number.
(a) 0
(b) 1
(c) No symbol
(d) None of the options
Answer: (b) 1
In simple words: In signed magnitude, a '1' in the very first bit of a binary number means that the number is negative. It acts like a minus sign.

🎯 Exam Tip: Remember that the leftmost bit (Most Significant Bit) acts as the sign bit in signed magnitude representation: 0 for positive and 1 for negative.

 

Question 98. In signed magnitude representation, ____ in the sign bit represents positive number.
(a) 0
(b) 1
(c) No symbol
(d) None of the options
Answer: (a) 0
In simple words: When a binary number uses signed magnitude, a '0' in the first bit means the number is positive. It tells us there's no minus sign.

🎯 Exam Tip: The sign bit is crucial in signed magnitude; distinguish between '0' for positive and '1' for negative numbers.

 

Question 99. The term data comes from the word ____.
(a) datum
(b) date
(c) fact
(d) None of the options
Answer: (a) datum
In simple words: The word "data" comes from "datum", which is the singular form meaning a single piece of raw fact or information.

🎯 Exam Tip: Understanding the origin of words like "data" (from "datum") can help you grasp their core meaning in computer science.

Part II

Very Short Answers.

 

Question 1. What is nibble?
Answer: A nibble is a small group of 4 bits. It is equal to half of a byte. Many systems use nibbles to represent digits in hexadecimal numbers.
In simple words: A nibble is just 4 bits, which is half of a byte.

🎯 Exam Tip: Remember the basic units of data storage: bit (1), nibble (4), byte (8), and their relationship.

 

Question 2. Define information.
Answer: Information is data that has been processed and organized, making it meaningful and useful. It is the output received from a computer after raw data is put in. This helps in understanding and making decisions.
In simple words: Information is processed data that has meaning and is useful.

🎯 Exam Tip: Clearly differentiate between raw "data" and processed, meaningful "information" in your answers.

 

Question 4. Define Bit and Byte.
Answer: A **Bit** is the smallest unit of data, short for "Binary digit", and can only be 0 or 1. It is the basic building block for all data in computers. A **Byte** is a collection of 8 bits and is the standard unit for measuring memory size in computers. One byte can represent a single character, like a letter or a number.
In simple words: A bit is a single 0 or 1. A byte is a group of 8 bits.

🎯 Exam Tip: Always remember that a byte consists of 8 bits, and this relationship is fundamental to computer memory measurement.

 

Question 5. Expand: BCD, EBCDIC, ASCII
Answer:
- **BCD** stands for Binary Coded Decimal.
- **EBCDIC** stands for Extended Binary Coded Decimal Interchange Code.
- **ASCII** stands for American Standard Code for Information Interchange.
These codes are essential for how computers store and represent characters and numbers.
In simple words: BCD, EBCDIC, and ASCII are different ways computers store information using codes.

🎯 Exam Tip: Practice writing out the full forms of common acronyms accurately, as they are often tested directly.

 

Question 6. What are the different types of coding schemes to represent the character sets?
Answer: The different coding schemes used to represent character sets in computers include:
- BCD (Binary Coded Decimal)
- EBCDIC (Extended Binary Coded Decimal Interchange Code)
- ASCII (American Standard Code for Information Interchange)
- Unicode
- ISCII (Indian Standard Code for Information Interchange)
These systems allow computers to store and display various characters, from English letters to symbols and letters from other languages.
In simple words: Computers use different codes like BCD, EBCDIC, ASCII, Unicode, and ISCII to show letters and symbols.

🎯 Exam Tip: When listing coding schemes, try to briefly explain their purpose or key feature if possible, to show a deeper understanding.

 

Question 7. What are the methods of converting a number from decimal to binary?
Answer: There are two main methods to convert a number from decimal (base 10) to binary (base 2):
1. **Repeated division by two:** This method involves repeatedly dividing the decimal number by 2 and collecting the remainders. The remainders, read in reverse order, form the binary equivalent.
2. **Sum of powers of 2:** This method involves finding which powers of 2 add up to the decimal number. For each power of 2 used, a '1' is placed in its corresponding binary position; otherwise, a '0' is used. Both methods help translate human-readable numbers into a format computers can understand.
In simple words: We can change decimal numbers to binary by either dividing by two many times or by adding up different powers of two.

🎯 Exam Tip: Understand both conversion methods thoroughly, as questions might ask you to apply a specific one or explain the procedure.

 

Question 8. What does base or radix mean?
Answer: The base, also called the radix, of a number system tells us how many unique digits or symbols are used in that system. It's the core idea behind positional numbering systems, where each digit's position carries a specific weight based on powers of the base. For example, in decimal (base 10), we use 10 digits (0-9).
In simple words: The base or radix of a number system is how many different digits it uses, like 10 for decimal numbers.

🎯 Exam Tip: When defining "base" or "radix", remember to mention its role in determining the number of digits and how positional values are assigned.

 

Question 9. What are the various ways for Binary representation of signed numbers?
Answer: Binary representation for signed numbers means how computers show positive and negative numbers. There are several ways to do this:
1. **Signed Magnitude representation:** The leftmost bit is used to indicate the sign (0 for positive, 1 for negative), and the rest of the bits represent the number's value.
2. **1's Complement:** Negative numbers are represented by inverting all the bits (changing 0s to 1s and 1s to 0s) of their positive equivalent.
3. **2's Complement:** This is the most common method. For a negative number, you find its 1's complement and then add 1 to it. This method simplifies arithmetic operations.
Each method has its own way of handling positive and negative values, crucial for computer calculations.
In simple words: Computers show positive and negative numbers in binary using signed magnitude, 1's complement, or 2's complement.

🎯 Exam Tip: Focus on understanding the distinct characteristics of each signed number representation method, especially the sign bit and how negative values are formed.

 

Question 10. Write a note on the decimal number system.
Answer: The decimal number system is the most common system we use every day, consisting of ten digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. It is also known as base 10. In this system, each digit's position gives it a specific value or "weight" based on powers of 10. For example, in the number 123, the '1' means \( 1 \times 10^2 \), the '2' means \( 2 \times 10^1 \), and the '3' means \( 3 \times 10^0 \). This positional value makes it easy to represent large numbers.
In simple words: The decimal system is our everyday number system using 10 digits (0-9), where each digit's place shows its value based on powers of 10.

🎯 Exam Tip: When describing number systems, always include the base (radix), the range of digits used, and how positional weights contribute to the number's value.

 

Question 12. How will you convert decimal to hexadecimal?
Answer: To convert a decimal number to hexadecimal (base 16), we use the "repeated division by 16" method. In this method, you continuously divide the decimal number by 16 and record the remainder. The process continues until the quotient becomes 0. The hexadecimal equivalent is then formed by reading the remainders from bottom to top. For remainders 10 through 15, use the hexadecimal symbols A through F respectively.
Example: Convert \( (31)_{10} \) into its equivalent hexadecimal number.
\[ \begin{array}{r|r} 16 & 31 \\ \cline{2-2} 16 & 1 \text{ Remainder } 15 \text{ (F)} \\ \cline{2-2} & 0 \text{ Remainder } 1 \text{ (1)} \\ \end{array} \]
Reading the remainders from bottom to top, we get \( (1F)_{16} \). This method is similar to decimal-to-binary conversion but uses 16 as the divisor.
Therefore, \( (31)_{10} = (1F)_{16} \).
In simple words: To change a decimal number to hexadecimal, keep dividing it by 16. Write down the remainders from bottom to top, using letters A-F for numbers 10-15.

🎯 Exam Tip: Remember to replace remainders 10-15 with their corresponding hexadecimal letters (A-F) when performing decimal to hexadecimal conversions.

 

Question 13. Give the procedure to convert Octal to Binary.
Answer: To convert an octal number to its binary equivalent, you simply take each octal digit and write its 3-digit binary representation. This is possible because \( 2^3 = 8 \), meaning three binary bits can represent one octal digit. You then combine all these 3-bit binary groups to form the complete binary number.
**Procedure:** For each octal digit in the given number, write its 3-digit binary equivalent using positional notation.
Example: Convert \( (6213)_8 \) to equivalent Binary number.
\[ \begin{array}{cccc} 6 & 2 & 1 & 3 \\ \downarrow & \downarrow & \downarrow & \downarrow \\ 110 & 010 & 001 & 011 \\ \end{array} \]
Therefore, \( (6213)_8 = (110010001011)_2 \).
In simple words: To change an octal number to binary, just replace each octal digit with its 3-bit binary code, then put all the binary codes together.

🎯 Exam Tip: Memorize the 3-bit binary equivalents for all octal digits (0-7) to speed up your conversions.

 

Question 15. Write short note on Binary Coded Decimal (BCD).
Answer: Binary Coded Decimal (BCD) is a system where each decimal digit (0-9) is represented by a 4-bit binary code. This encoding system can handle \( 2^4 = 16 \) possible values, but only 10 are used for decimal digits. This method is useful for applications where decimal arithmetic is important, like in calculators or digital clocks, as it simplifies the conversion between decimal and binary. However, BCD is not widely used in general computing today due to less efficient storage.
In simple words: BCD is a code that uses 4 binary bits to represent each decimal digit.

🎯 Exam Tip: Remember that BCD represents *each* decimal digit separately with 4 bits, which is different from converting a whole decimal number to binary.

 

Question 16. Write note on EBCDIC encoding system.
Answer: The Extended Binary Coded Decimal Interchange Code (EBCDIC) is an 8-bit character encoding system, developed by IBM. It is similar to ASCII but uses a different set of codes. EBCDIC can represent 256 ( \( 2^8 \) ) different characters. It was mainly used on IBM mainframe operating systems and compatible machines. Although ASCII is more common today, EBCDIC played a significant role in early computing by allowing a wide range of characters to be represented.
In simple words: EBCDIC is an old 8-bit code by IBM that computers used to show up to 256 different characters.

🎯 Exam Tip: Key points for EBCDIC are its 8-bit nature, IBM origin, and its ability to represent 256 characters, distinct from ASCII.

Part III

III. Very Short Answers

 

Question 1. Write about the binary number system.
Answer: The binary number system is a base-2 system, meaning it uses only two digits: 0 and 1. These digits are called bits. In this system, numbers are represented using powers of 2. The leftmost bit in a binary number is called the Most Significant Bit (MSB) because it carries the largest positional weight. Conversely, the rightmost bit is the Least Significant Bit (LSB) and holds the smallest positional weight. This system is the fundamental language of computers.
\[ \begin{array}{|c|c|c|c|} \hline \mathbf{1} & \mathbf{1} & \mathbf{0} & \mathbf{1} \\ \hline \text{MSB} & & & \text{LSB} \\ \hline \end{array} \]
In simple words: The binary system uses only 0s and 1s. The bit on the far left is most important, and the bit on the far right is least important.

🎯 Exam Tip: Always state the base (2) and the digits (0, 1) when describing the binary system, and know the terms MSB and LSB.

 

Question 2. What is the octal number system?
Answer: The octal number system is a base-8 system, meaning it uses eight unique digits: 0, 1, 2, 3, 4, 5, 6, and 7. Each digit in an octal number has a positional value that is a power of 8. This system is often used as a compact way to represent binary numbers, as three binary bits can represent one octal digit (since \( 2^3 = 8 \)). It helps in making binary sequences shorter and easier to read.
In simple words: The octal system uses digits 0-7, where each digit's position is based on powers of 8.

🎯 Exam Tip: Remember that octal is base 8 and uses digits 0-7, and it's commonly used to simplify the representation of binary numbers.

 

Question 3. Give the procedure to convert decimal to octal.
Answer: To convert a decimal number to an octal number (base 8), you use the "repeated division by 8" method. In this process, you continuously divide the decimal number by 8 and record the remainder after each division. You keep dividing the quotient until it becomes 0. The octal equivalent is then formed by reading all the remainders from the last one (bottom) to the first one (top). This systematic division ensures an accurate conversion.
Example: Convert \( (65)_{10} \) into its equivalent Octal number.
\[ \begin{array}{r|r} 8 & 65 \\ \cline{2-2} 8 & 8 \text{ Remainder } 1 \text{ (LSB)} \\ \cline{2-2} & 1 \text{ Remainder } 0 \\ \cline{2-2} & 0 \text{ Remainder } 1 \text{ (MSB)} \\ \end{array} \]
Reading the remainders from bottom to top, we get \( (101)_8 \).
Therefore, \( (65)_{10} = (101)_8 \).
In simple words: To convert decimal to octal, divide the decimal number by 8 repeatedly and write down the remainders from bottom to top.

🎯 Exam Tip: When converting, ensure you read the remainders from the last one obtained (MSB) to the first one (LSB) to get the correct order of digits.

 

Question 4. Give the procedure to convert Octal to Decimal.
Answer: To convert an octal number to its decimal equivalent, we use the positional notation method. This method involves multiplying each digit of the octal number by the corresponding power of its base (which is 8). The powers of 8 start from \( 8^0 \) for the rightmost digit and increase by one for each position to the left. Finally, all these products are added together to get the decimal number. This is a common way to understand the true value of a number in a different base.
**Procedure:**
- Write down the octal digits and list the powers of 8 from right to left (positional notation).
- For each positional notation of the digit, write the equivalent weight.
- Multiply each octal digit with its corresponding weight.
- Add all the values.
Example: Convert \( (1265)_8 \) to equivalent Decimal number.

So, \( (1265)_8 = (512 \times 1) + (64 \times 2) + (8 \times 6) + (1 \times 5) \)
\( = 512 + 128 + 48 + 5 \)
\( = (693)_{10} \).
In simple words: To change octal to decimal, multiply each octal digit by 8 raised to its position's power, then add all the results.

🎯 Exam Tip: Clearly write out the powers of 8 for each position and perform multiplication and addition carefully to avoid errors.

 

Question 5. How will you convert Hexadecimal to Decimal?
Answer: To convert a hexadecimal number to its decimal equivalent, you use the positional notation method, similar to octal to decimal conversion but with a base of 16. Each hexadecimal digit is multiplied by its corresponding power of 16. The powers of 16 start from \( 16^0 \) for the rightmost digit and increase by one for each position to the left. Remember to convert hexadecimal letters (A-F) to their decimal values (10-15) before multiplying. Finally, all these products are added together to get the decimal number. This process helps translate machine-level hex values into human-readable decimal form.
**Procedure:**
- Write down the hexadecimal digits and list the powers of 16 from right to left (positional notation).
- For each positional notation written for the digit, now write the equivalent weight.
- Multiply each digit with its corresponding weight.
- Add all the values to get one final value.
Example: Convert \( (25F)_{16} \) into its equivalent Decimal number.

So, \( (25F)_{16} = (2 \times 256) + (5 \times 16) + (15 \times 1) \)
\( = 512 + 80 + 15 \)
\( = (607)_{10} \).
In simple words: To change hexadecimal to decimal, multiply each hex digit (after changing letters to numbers) by 16 raised to its position's power, then add them all up.

🎯 Exam Tip: Always remember to convert hexadecimal letters (A-F) to their decimal equivalents (10-15) *before* performing multiplication.

 

Question 6. Write about binary representation for signed numbers.
Answer: Binary representation for signed numbers deals with how computers store both positive and negative integer values. The simplest way to do this is called **Signed Magnitude** representation. In this method, the leftmost bit of the binary number is reserved as a sign bit: a '0' indicates a positive number, while a '1' indicates a negative number. The remaining bits represent the actual value (magnitude) of the number. For example, in an 8-bit system, 7 bits are for the value, and 1 bit is for the sign. However, this method has a drawback, such as having two representations for zero (+0 and -0), and complex addition/subtraction. Other methods like 1's complement and 2's complement address these issues. The computer uses these representations to perform calculations on signed numbers effectively.
The numbers are represented in computers in different ways:
- Signed Magnitude representation
- 1's Complement
- 2's Complement
In simple words: Signed numbers in binary mean showing positive and negative numbers. Signed magnitude uses the first bit to show if a number is plus (0) or minus (1).

🎯 Exam Tip: Understand that the sign bit is usually the leftmost bit, and its value (0 or 1) determines whether the number is positive or negative in signed magnitude representation.

 

Question 7. Explain ASCII code in detail.
Answer: ASCII, which stands for American Standard Code for Information Interchange, is a very popular character encoding system widely used in computers. Most computers use this system. The original ASCII was a 7-bit code, meaning it could represent \( 2^7 = 128 \) different characters, including English letters (uppercase and lowercase), numbers, punctuation marks, and control characters. For example, the uppercase letter 'A' has an ASCII value of 65. The binary representation for 'A' (in 7 bits) is 1000001. A later extended version, ASCII-8, uses 8 bits and can represent 256 characters ( \( 2^8 = 256 \) ), allowing for additional symbols and characters, like 01000001 for 'A'. This code makes sure that different computers can understand the same text.
In simple words: ASCII is a popular code that uses 7 or 8 bits to represent English letters, numbers, and symbols so computers can read text.

🎯 Exam Tip: Remember ASCII as a 7-bit (128 characters) or 8-bit (256 characters) code primarily for English and basic symbols, and know its full form.

 

Question 8. Explain Unicode in detail.
Answer: Unicode is a modern and comprehensive character encoding system designed to handle all the coding systems of universal languages. Unlike ASCII, which can only represent 256 characters (mostly English and European languages), Unicode uses 16 bits or more, allowing it to represent up to 65,536 ( \( 2^{16} \) ) characters in its basic form (UTF-16). This means it can include characters from virtually all written languages in the world, like Tamil, Malayalam, Kannada, and Telugu, which could not be represented by ASCII. Unicode is widely used in most modern computers and on the internet to ensure text can be displayed correctly across different systems and languages. It is often denoted by hexadecimal numbers. This allows for a global standard for text encoding.
In simple words: Unicode is a special code for computers that can show characters from almost all languages in the world, not just English.

🎯 Exam Tip: Highlight Unicode's key advantage: its ability to represent a vast number of characters from multiple languages, contrasting it with ASCII's limitations.

Part IV

IV. Detail Answers.

 

Question 1. Explain decimal to binary conversion using Repeated Division by 2 methods.
Answer: The "Repeated Division by 2" method is a common way to convert a decimal number to its binary equivalent. In this procedure, you take the decimal number and continuously divide it by 2. After each division, you note down the remainder, which will always be either 0 or 1. You continue this process with the new quotient until the quotient itself becomes 0 or 1. The binary equivalent is formed by writing the remainders in reverse order, starting from the last remainder (which is the most significant bit, MSB) up to the first remainder (the least significant bit, LSB). This method is very systematic and reliable. For example, if the last quotient is '0' or '1', that value also acts as a final remainder and is included. This ensures all parts of the number are converted accurately.
Example: Convert \( (65)_{10} \) into its equivalent binary number.
In simple words: To change a decimal number to binary, divide it by 2 over and over. Write down each remainder, and when you're done, read the remainders backwards to get the binary number.

🎯 Exam Tip: Always remember to collect the remainders and read them from bottom-to-top (last remainder to first remainder) to get the correct binary sequence.

 

Question 2. Explain decimal to binary conversion using Sum of powers of 2 methods.
Answer: The "Sum of powers of 2" method is another way to convert a decimal number into its binary form. In this method, you identify which powers of 2 (like \( 2^0, 2^1, 2^2, 2^3 \), etc.) add up to the decimal number you want to convert. You start by finding the largest power of 2 that is less than or equal to the decimal number. If that power of 2 is used, you place a '1' in its corresponding binary position. Then, you subtract that power of 2 from the decimal number and repeat the process with the remaining value. If a power of 2 is not used, you place a '0' in its position. This continues until the decimal number becomes 0. This method helps visualize the binary representation by showing the "on" (1) and "off" (0) states for each power of two.
Example: Convert \( (65)_{10} \) to binary using sum of powers of 2.

a) Find the largest power of 2 that is smaller than or equal to 65. That is \( 2^6 = 64 \).
\( 65_{10} > 64_{10} \)
b) Set the \( 2^6 \) (64's) bit to 1 and subtract 64 from the original number.
\( 65 - 64 = 1 \)
c) \( 2^5 = 32 \). 32 is greater than the remaining total (1). Therefore, set the \( 2^5 \) (32's) bit to 0.
d) \( 2^4 = 16 \). 16 is greater than the remaining total (1). Therefore, set the \( 2^4 \) (16's) bit to 0.
e) \( 2^3 = 8 \). 8 is greater than the remaining total (1). Therefore, set the \( 2^3 \) (8's) bit to 0.
f) \( 2^2 = 4 \). 4 is greater than the remaining total (1). Therefore, set the \( 2^2 \) (4's) bit to 0.
g) \( 2^1 = 2 \). 2 is greater than the remaining total (1). Therefore, set the \( 2^1 \) (2's) bit to 0.
h) \( 2^0 = 1 \). As the remaining value is equivalent to the 1's bit, set it to 1.
\( 1 - 1 = 0 \)
The conversion is complete. The binary number is formed by combining these bits.

Therefore, \( (65)_{10} = (1000001)_2 \).
In simple words: To change a decimal number to binary using powers of 2, find which powers of 2 add up to your number. Put a '1' for powers you use and a '0' for powers you don't.

🎯 Exam Tip: Always list out the powers of 2 from largest to smallest (or vice-versa) to systematically determine which ones contribute to the decimal number.

 

Question 3. Explain the procedure to convert fractional decimal to Binary.
Answer: To convert a fractional decimal number (a decimal number with a part after the decimal point) to binary, we use the method of repeated multiplication by 2. This is different from integer conversion. Here's how it works:
**The steps involved in the method of repeated multiplication by 2:**
1. **Step 1:** Multiply the decimal fraction by 2 and note the integer part of the result. This integer part will be either 0 or 1.
2. **Step 2:** Discard the integer part from the previous product. Now, multiply only the remaining fractional part by 2 again. Repeat Step 1 until the fractional part becomes 0 (terminates) or until the same fractional part starts repeating. Sometimes, you might need to stop after a certain number of binary digits if it does not terminate.
3. **Step 3:** The collected integer parts (0s and 1s) form the binary equivalent of the decimal fraction. These are the digits that will appear after the binary point.
4. **Step 4:** The final answer is written by taking the integer parts obtained from top to bottom (first integer part to last integer part). This sequence represents the fractional binary part. This method carefully extracts each binary digit after the decimal point.
Example: Convert \( (0.2)_{10} \) to binary.
\[ \begin{array}{rll} 0.2 \times 2 &= (0.4) & \text{Integer part } 0 \text{ (first integer part obtained)} \\ 0.4 \times 2 &= (0.8) & \text{Integer part } 0 \\ 0.8 \times 2 &= (1.6) & \text{Integer part } 1 \\ 0.6 \times 2 &= (1.2) & \text{Integer part } 1 \\ 0.2 \times 2 &= (0.4) & \text{Integer part } 0 \text{ (last integer part obtained, repeats)} \\ \end{array} \]
Write the integer parts from top to bottom to obtain the equivalent fractional binary number. So, the sequence of integer parts is 00110...
Hence, \( (0.2)_{10} = (0.00110011...)_2 \). This number is repeating because 0.2 kept coming back.
In simple words: To change a decimal fraction to binary, multiply the fraction by 2 many times. Write down the integer part (0 or 1) each time, and read them from top to bottom.

🎯 Exam Tip: For fractional conversions, multiply by 2 and collect integer parts from top to bottom. Be careful with repeating fractions; a bar notation is used if they repeat infinitely.

 

Question 4. How will you convert Binary to Decimal?
Answer: To convert a binary number to its decimal equivalent, we use the positional notation method. This process involves assigning a power of 2 to each bit in the binary number, starting from the rightmost bit. For integers, the powers of 2 start from \( 2^0 \) and increase by one for each position to the left. For fractional parts (after the binary point), powers of 2 are negative (e.g., \( 2^{-1}, 2^{-2} \)). Each binary digit (0 or 1) is multiplied by its corresponding positional weight (the power of 2). Finally, all these products are added together to get the decimal number. This method directly translates the binary representation into its base-10 value.
**Procedure:**
1. **Step 1:** Write down the binary digits and list the powers of 2 from right to left (positional notation).
2. **Step 2:** For each positional notation written for the digit, write the equivalent weight.
3. **Step 3:** Multiply each binary digit (0 or 1) with its corresponding weight.
4. **Step 4:** Add all the values.
Example: Convert \( (111011)_2 \) to decimal.

So, \( (111011)_2 = (1 \times 32) + (1 \times 16) + (1 \times 8) + (0 \times 4) + (1 \times 2) + (1 \times 1) \)
\( = 32 + 16 + 8 + 0 + 2 + 1 \)
\( = (59)_{10} \).
In simple words: To change a binary number to decimal, multiply each 0 or 1 by its place value (powers of 2), then add all those results together.

🎯 Exam Tip: Always remember that the rightmost bit corresponds to \( 2^0 \), and the powers of 2 increase as you move left.

 

Question 5. How will you convert Binary to Octal?
Answer: To convert a binary number to an octal number, follow these steps:
1. Group the binary number into sets of three bits, starting from the right side.
2. If the leftmost group has fewer than three bits, add leading zeros to make it a full three-bit group.
3. Convert each three-bit binary group into its equivalent octal digit. You can use a table of 2's power positional weights (4-2-1) for this.
For example, to convert \( (11010110)_2 \) to an octal number:
Group into 3 bits from right: \( \underbrace{11}_{011} \underbrace{010}_{010} \underbrace{110}_{110} \)
Adding leading zero to the first group: \( \underbrace{011}_{3} \underbrace{010}_{2} \underbrace{110}_{6} \)
So, \( (11010110)_2 = (326)_8 \). The digits in octal go from 0 to 7.
In simple words: To change a binary number to octal, you split it into groups of three digits from the right. If the first group is too short, add zeros. Then, change each three-digit binary group into one octal digit.

🎯 Exam Tip: Always remember that octal uses base 8, so each binary group must be exactly 3 bits long because \( 2^3 = 8 \).

 

Question 6. Give the procedure to convert Binary to Hexadecimal.
Answer: To convert a binary number to a hexadecimal number, follow these steps:
1. Group the binary number into sets of four bits, starting from the right side.
2. If the leftmost group has fewer than four bits, add leading zeros to make it a full four-bit group.
3. Convert each four-bit binary group into its equivalent hexadecimal digit. You can use a table of 2's power positional weights (8-4-2-1) for this. Hexadecimal digits include 0-9 and A-F for 10-15.
For example, to convert \( (1111010110)_2 \) to a hexadecimal number:
Group into 4 bits from right: \( \underbrace{11}_{0011} \underbrace{1101}_{1101} \underbrace{0110}_{0110} \)
Adding leading zeros to the first group: \( \underbrace{0011}_{3} \underbrace{1101}_{D} \underbrace{0110}_{6} \)
So, \( (1111010110)_2 = (3D6)_{16} \).
In simple words: To change a binary number to hexadecimal, divide it into groups of four digits from the right. Add leading zeros if needed. Then, change each four-digit binary group into one hexadecimal digit.

🎯 Exam Tip: Hexadecimal uses base 16, so each binary group must be exactly 4 bits long because \( 2^4 = 16 \).

 

Question 7. Give the procedure to convert fractional Binary to Decimal equivalent.
Answer: To convert a fractional binary number to its decimal equivalent, follow these steps:
1. Convert the integral (whole number) part of the binary number to decimal using the positional notation method (powers of 2, like \( 2^0, 2^1, 2^2 \), etc.).
2. To convert the fractional part of the binary number to decimal:
a. Write down the binary digits in the fractional part.
b. Assign positional weights to these digits using negative powers of 2, starting from \( 2^{-1} \) (which is 0.5) for the first digit after the decimal point, then \( 2^{-2} \) (0.25), \( 2^{-3} \) (0.125), and so on.
c. Multiply each fractional binary digit by its corresponding positional weight.
d. Add all these multiplied values together.
3. The final answer is obtained by combining the converted integral part, a decimal point, and the sum from the fractional part.
For example, to convert \( (11.011)_2 \) to its decimal equivalent:
Integral part \( (11)_2 = (1 \times 2^1) + (1 \times 2^0) = 2 + 1 = 3 \).
Fractional part \( (0.011)_2 = (0 \times 2^{-1}) + (1 \times 2^{-2}) + (1 \times 2^{-3}) \)
\( = (0 \times 0.5) + (1 \times 0.25) + (1 \times 0.125) \)
\( = 0 + 0.25 + 0.125 = 0.375 \).
So, \( (11.011)_2 = 3.375_{10} \). This process combines the whole and fractional parts accurately.
In simple words: To change a binary number with a decimal point to decimal, first convert the whole number part normally. Then, for the digits after the point, multiply each by a decreasing power of two (like 1/2, 1/4, 1/8) and add them up. Combine both results.

🎯 Exam Tip: Remember that binary fractional positions start with \( 2^{-1} \) (0.5), not \( 2^0 \), and decrease to the right.

 

Question 8. Explain the method of representing signed binary numbers in the Signed Magnitude representation.
Answer: The simplest way to show negative binary numbers is called Signed Magnitude representation. In this method, the leftmost bit (the Most Significant Bit or MSB) acts as a sign bit. If this sign bit is 0, the number is positive. If it is 1, the number is negative. The remaining bits store the actual value or magnitude of the number.
For example, using an 8-bit system, where 1 bit is for the sign and 7 bits are for the value:
To represent +43:
Sign bit: 0 (for positive)
Magnitude of 43 in binary: 0101011 (using 7 bits)
So, +43 in 8-bit signed magnitude is \( 00101011 \).
To represent -43:
Sign bit: 1 (for negative)
Magnitude of 43 in binary: 0101011 (using 7 bits)
So, -43 in 8-bit signed magnitude is \( 10101011 \). This method clearly separates the sign from the number's value.
In simple words: Signed magnitude uses the first bit to show if a number is positive (0) or negative (1). The rest of the bits show the number's actual value.

🎯 Exam Tip: In signed magnitude, the magnitude part is always the positive binary equivalent of the number, regardless of its sign.

 

Question 9. Explain the method of representing signed binary numbers in 1's complement representation.
Answer: The 1's complement method is another way to represent signed numbers, especially negative ones. This approach is primarily used for negative numbers where the Most Significant Bit (MSB) is 1. To find the 1's complement of a number, you simply invert all its bits.
The steps to find the 1's complement of a number are:
1. Convert the given decimal number into its binary form.
2. Make sure the binary number has 8 bits. If it has fewer, add zeros to the left (MSB side) until it becomes an 8-bit number.
3. Invert all the bits: change every 1 to a 0 and every 0 to a 1.
For example, to find the 1's complement for \( (-24)_{10} \):
Binary number for +24: \( (00011000)_2 \) (in 8-bit format).
To find 1's complement of -24, invert all bits of +24:
\( 00011000 \rightarrow 11100111 \)
So, the 1's complement of \( (-24)_{10} \) is \( (11100111)_2 \). This method provides a straightforward way to represent negative values by simply flipping bits.
In simple words: To get the 1's complement of a negative number, first write its positive binary form with 8 bits. Then, just flip all the 0s to 1s and all the 1s to 0s.

🎯 Exam Tip: Remember that 1's complement is derived directly by inverting bits, which simplifies some binary arithmetic operations.

 

Question 10. Explain the method of representing signed binary numbers in 2's complement representation.
Answer: The 2's complement method is a widely used way to represent signed binary numbers, especially negative numbers in computers. It offers advantages in simplifying addition and subtraction operations. For a negative number, its 2's complement is found by first taking the 1's complement and then adding 1 to the result.
The procedure for finding the 2's complement of a number is as follows:
1. Invert all the bits of the positive binary sequence (this is the 1's complement). This means changing every 0 to 1 and every 1 to 0.
2. Add 1 to the Least Significant Bit (LSB) of the 1's complement result.
For example, to represent \( (-24)_{10} \) in 2's complement:
Binary equivalent of +24 (8-bit format): \( 00011000 \).
1's complement of \( (-24)_{10} \): \( 11100111 \) (by inverting bits).
Add 1 to the LSB:
    \( 11100111 \)
    \( +         1 \)
    \( -------- \)
    \( 11101000 \)
So, the 2's complement of \( (-24)_{10} \) is \( (11101000)_2 \). This representation makes binary arithmetic more efficient.
In simple words: To get the 2's complement of a number, first find its 1's complement (flip all bits). Then, just add 1 to the very last digit.

🎯 Exam Tip: A key difference is that 2's complement has only one representation for zero, unlike 1's complement which has both positive and negative zero.

 

Question 11. Explain binary addition with a suitable example.
Answer: Binary addition is the process of adding binary numbers, which only use the digits 0 and 1. It follows rules similar to decimal addition, but with only two digits. When the sum of bits is 2 (which is \( 1+1 \)), it results in a sum of 0 and a carry of 1 to the next position. The core rules for binary addition are:

When adding two numbers, if \( 1+1=10 \) in binary, it means the sum is 0, and there is a carry-over of 1 to the next left position. This carry bit is then added to the bits in the next column.
For example, let's add \( (1011)_2 \) and \( (1001)_2 \):
   Carry: \( 1 \quad 1 \)
          \( 1011 \)
      \( + 1001 \)
      \( -------- \)
      \( 10100 \)
So, \( (1011)_2 + (1001)_2 = (10100)_2 \). The carry bit moves just like in decimal addition.
Another example, adding \( (23)_{10} \) and \( (12)_{10} \):
First, convert decimal numbers to binary:
For \( (23)_{10} \):

So, \( (23)_{10} = (00010111)_2 \).
For \( (12)_{10} \):

So, \( (12)_{10} = (00001100)_2 \).
Now, perform binary addition of \( (23)_{10} \) and \( (12)_{10} \):

So, \( (35)_{10} = (0100011)_2 \).
In simple words: Binary addition is like regular addition but only with 0s and 1s. If you add 1 and 1, the result is 0 and you carry over a 1 to the next spot, just like carrying over 10 in decimal.

🎯 Exam Tip: Practice binary addition using both small numbers and those requiring multiple carry-overs to fully understand the concept.

 

Question 11. Explain binary subtraction with a suitable example.
Answer: Binary subtraction is the process of subtracting binary numbers. It also uses rules similar to decimal subtraction, but involves only 0s and 1s. The key concept here is 'borrowing' when a larger digit needs to be subtracted from a smaller one. The basic rules for binary subtraction are:

When you need to subtract 1 from 0, you must borrow from the next more significant bit to the left. When borrowing from a 1, that 1 becomes 0. If you borrow from a 0, that 0 becomes 1 and you must continue borrowing from the next bit to its left until you find a 1 to borrow from, turning all intermediate 0s into 1s.
For example, subtract \( (10100)_2 \) from \( (1001010)_2 \):
      \( \overset{0}{1} \overset{10}{0} \overset{0}{0} \overset{10}{1} 0 \)
    \( -     010100 \)
    \( -------- \)
      \( 0110001 \)
So, \( (1001010)_2 - (10100)_2 = (0110001)_2 \).
For another example, to calculate \( (-21)_{10} + (5)_{10} \):
Step 1: Convert -21 and 5 into binary form. We'll use 2's complement for negative numbers.
Binary of \( (21)_{10} \): \( (10101)_2 \). In 8-bit format: \( (00010101)_2 \).
1's complement of \( (-21)_{10} \): \( (11101010)_2 \).
2's complement of \( (-21)_{10} \): \( (11101010)_2 + 1 = (11101011)_2 \).
Binary of \( (5)_{10} \): \( (101)_2 \). In 8-bit format: \( (00000101)_2 \).
Step 2: Perform Binary Addition of \( (-21)_{10} \) and \( (5)_{10} \):

The result \( (11110000)_2 \) is the 2's complement of \( (-16)_{10} \).
In simple words: Binary subtraction is like regular subtraction, but when you need to subtract 1 from 0, you 'borrow' from the next digit. If there's a 1 to borrow from, it becomes 0. If it's a 0, it becomes 1, and you keep borrowing from the left.

🎯 Exam Tip: For subtraction involving negative numbers, it's often easiest to convert both numbers to their 2's complement form and then perform binary addition.

 

Workshop

 

Question 1. Identify the number system for the following numbers.
Answer:

In simple words: Each number has a small number written at the bottom right. This small number tells you what type of number system it belongs to, like base 10 for decimal or base 2 for binary.

🎯 Exam Tip: The subscript number (like the '10' in \( (1010)_{10} \)) always indicates the base of the number system.

 

Question 2. State whether the following numbers are valid or not. If invalid, give a reason.
Answer:

In simple words: We check if the digits in a number are allowed for its type of number system. For example, octal numbers can only have digits from 0 to 7, so an 8 or 9 makes it wrong.

🎯 Exam Tip: Always remember the valid digit range for each number system: Binary (0-1), Octal (0-7), Decimal (0-9), Hexadecimal (0-9, A-F).

 

Question 3. Convert the following Decimal numbers to their equivalent Binary, Octal, Hexadecimal.
(i) 1920
(ii) 255
(iii) 126
Answer:
(i) Convert \( (1920)_{10} \) to Binary, Octal, and Hexadecimal:
Conversion to Binary (Repeated Division by 2):

Conversion to Octal (Repeated Division by 8):

Conversion to Hexadecimal (Repeated Division by 16):

Therefore, \( (1920)_{10} = (11110000000)_2 = (3600)_8 = (780)_{16} \).

(ii) Convert \( (255)_{10} \) to Binary, Octal, and Hexadecimal:
Conversion to Binary (Repeated Division by 2):

Conversion to Octal (Repeated Division by 8):

Conversion to Hexadecimal (Repeated Division by 16):

Therefore, \( (255)_{10} = (11111111)_2 = (377)_8 = (FF)_{16} \).

(iii) Convert \( (126)_{10} \) to Binary, Octal, and Hexadecimal:
Conversion to Binary (Repeated Division by 2):

Conversion to Octal (Repeated Division by 8):

Conversion to Hexadecimal (Repeated Division by 16):

Therefore, \( (126)_{10} = (1111110)_2 = (176)_8 = (7E)_{16} \).
In simple words: To change a decimal number into binary, octal, or hexadecimal, you keep dividing it by the base of the new system (2, 8, or 16) and note the remainders. Read the remainders from bottom to top to get the new number.

🎯 Exam Tip: Always remember to collect the remainders from bottom to top for the final converted number. For hexadecimal, use A-F for values 10-15.

 

Question 4. Convert the given Binary number into its equivalent Decimal, Octal, and Hexadecimal numbers.
(i) 101110101
(ii) 1011010
(iii) 101011111
Answer:
(i) Convert \( (101110101)_2 \) to Decimal, Octal, and Hexadecimal:
Binary to Decimal (Multiply by positional value and then add):
\( (101110101)_2 = (1 \times 2^8) + (0 \times 2^7) + (1 \times 2^6) + (1 \times 2^5) + (1 \times 2^4) + (0 \times 2^3) + (1 \times 2^2) + (0 \times 2^1) + (1 \times 2^0) \)
\( = 256 + 0 + 64 + 32 + 16 + 0 + 4 + 0 + 1 = 373 \).
Binary to Octal (Group into 3 bits):
Group: \( \underbrace{101}_{5} \underbrace{110}_{6} \underbrace{101}_{5} \)
So, \( (101110101)_2 = (565)_8 \).
Binary to Hexadecimal (Group into 4 bits):
Group: \( \underbrace{0001}_{1} \underbrace{0111}_{7} \underbrace{0101}_{5} \)
Adding leading zeros: \( \underbrace{0001}_{1} \underbrace{0111}_{7} \underbrace{0101}_{5} \)
So, \( (101110101)_2 = (175)_{16} \).

(ii) Convert \( (1011010)_2 \) to Decimal, Octal, and Hexadecimal:
Binary to Decimal (Multiply by positional value and then add):
\( (1011010)_2 = (1 \times 2^6) + (0 \times 2^5) + (1 \times 2^4) + (1 \times 2^3) + (0 \times 2^2) + (1 \times 2^1) + (0 \times 2^0) \)
\( = 64 + 0 + 16 + 8 + 0 + 2 + 0 = 90 \).
Binary to Octal (Group into 3 bits):
Group: \( \underbrace{001}_{1} \underbrace{011}_{3} \underbrace{010}_{2} \)
Adding leading zeros: \( \underbrace{001}_{1} \underbrace{011}_{3} \underbrace{010}_{2} \)
So, \( (1011010)_2 = (132)_8 \).
Binary to Hexadecimal (Group into 4 bits):
Group: \( \underbrace{0101}_{5} \underbrace{1010}_{A} \)
Adding leading zeros: \( \underbrace{0101}_{5} \underbrace{1010}_{A} \)
So, \( (1011010)_2 = (5A)_{16} \).

(iii) Convert \( (101011111)_2 \) to Decimal, Octal, and Hexadecimal:
Binary to Decimal (Multiply by positional value and then add):
\( (101011111)_2 = (1 \times 2^8) + (0 \times 2^7) + (1 \times 2^6) + (0 \times 2^5) + (1 \times 2^4) + (1 \times 2^3) + (1 \times 2^2) + (1 \times 2^1) + (1 \times 2^0) \)
\( = 256 + 0 + 64 + 0 + 16 + 8 + 4 + 2 + 1 = 351 \).
Binary to Octal (Group into 3 bits):
Group: \( \underbrace{101}_{5} \underbrace{011}_{3} \underbrace{111}_{7} \)
So, \( (101011111)_2 = (537)_8 \).
Binary to Hexadecimal (Group into 4 bits):
Group: \( \underbrace{0001}_{1} \underbrace{0101}_{5} \underbrace{1111}_{F} \)
Adding leading zeros: \( \underbrace{0001}_{1} \underbrace{0101}_{5} \underbrace{1111}_{F} \)
So, \( (101011111)_2 = (15F)_{16} \).
In simple words: To change a binary number to decimal, multiply each digit by its power of 2 and add them up. For octal, split the binary number into groups of three digits. For hexadecimal, split into groups of four digits. Then, convert each group to its single octal or hexadecimal digit.

🎯 Exam Tip: Always check your groupings carefully for octal (3 bits) and hexadecimal (4 bits), and ensure leading zeros are added if a group is incomplete.

 

Question 5. Convert the following Octal numbers into Binary numbers.
a) 472
b) 145
c) 347
d) 6247
e) 645
Answer: To convert an octal number to a binary number, simply write the three-digit binary equivalent for each octal digit. The procedure is:
1. For each octal digit in the given number, write its corresponding three-digit binary number.
2. Combine these three-digit binary numbers in the same order to form the final binary equivalent.

a) Convert \( (472)_8 \) to Binary:
Octal Digit:
\( 4 \quad 7 \quad 2 \)
3-digit Binary Number:
\( 100 \quad 111 \quad 010 \)
So, \( (472)_8 = (100111010)_2 \).

b) Convert \( (145)_8 \) to Binary:
Octal Digit:
\( 1 \quad 4 \quad 5 \)
3-digit Binary Number:
\( 001 \quad 100 \quad 101 \)
So, \( (145)_8 = (001100101)_2 \).

c) Convert \( (347)_8 \) to Binary:
Octal Digit:
\( 3 \quad 4 \quad 7 \)
3-digit Binary Number:
\( 011 \quad 100 \quad 111 \)
So, \( (347)_8 = (011100111)_2 \).

d) Convert \( (6247)_8 \) to Binary:
Octal Digit:
\( 6 \quad 2 \quad 4 \quad 7 \)
3-digit Binary Number:
\( 110 \quad 010 \quad 100 \quad 111 \)
So, \( (6247)_8 = (110010100111)_2 \).

e) Convert \( (645)_8 \) to Binary:
Octal Digit:
\( 6 \quad 4 \quad 5 \)
3-digit Binary Number:
\( 110 \quad 100 \quad 101 \)
So, \( (645)_8 = (110100101)_2 \).
In simple words: To change an octal number to binary, replace each octal digit with its three-digit binary equivalent. Just stick these binary groups together to get the final binary number.

🎯 Exam Tip: Remember the 3-bit binary equivalents for all octal digits (0-7) to quickly perform these conversions. For example, 0 is 000, 1 is 001, 7 is 111.

 

Question 6. Convert the following Hexadecimal numbers to Binary numbers
a) A6
b) BE
c) 9BC8
d) BC9
Answer:
Procedure: To convert a hexadecimal number to binary, write the four-digit binary equivalent for each hexadecimal digit. This will give the equivalent binary number. For example, 'A' in hexadecimal is '1010' in binary, and '6' is '0110'. The computer then combines these binary parts.
a) A6
Hexadecimal Digit: A 6
4 digit Binary number: 1010 0110
(A6)\(_{16}\) = (10100110)\(_{2}\).
b) BE
Hexadecimal Digit: B E
4 digit Binary number: 1011 1110
(BE)\(_{16}\) = (10111110)\(_{2}\).
c) 9BC8
Hexadecimal Digit: 9 B C 8
4 digit Binary number: 1001 1011 1100 1000
(9BC8)\(_{16}\) = (1001101111001000)\(_{2}\).
d) BC9
Hexadecimal Digit: B C 9
4 digit Binary number: 1011 1100 1001
(BC9)\(_{16}\) = (101111001001)\(_{2}\).
In simple words: For each digit in the hexadecimal number, write down its four-digit binary form. Then, put all these binary parts together to get the full binary number.

🎯 Exam Tip: Always remember the 4-bit binary equivalents for hexadecimal digits 0-F. This is a fundamental conversion for computer science.

 

Question 7. Write the 1's complement number and 2's complement number for the following decimal numbers:
Perform the following binary computations:
a) -22
b) -13
c) -65
d) -46
Answer:
To find the 1's and 2's complement of a negative decimal number, first convert its positive equivalent to binary. Then, find the 1's complement by inverting all bits (0s become 1s, and 1s become 0s). The 2's complement is found by adding 1 to the 1's complement. This process helps represent negative numbers in computers.
a) -22

Binary of 22: 10110
8-digit binary of 22: 00010110
1's complement of -22: 11101001
2's complement of -22: 11101001 + 1
\( \implies \) 11101010

b) -13
Binary of 13: 1101
8-digit binary of 13: 00001101
1's complement of -13: 11110010
2's complement of -13: 11110010 + 1
\( \implies \) 11110011

c) -65
Binary of 65: 1000001
8-digit binary of 65: 01000001
1's complement of -65: 10111110
2's complement of -65: 10111110 + 1
\( \implies \) 10111111

d) -46
Binary of 46: 101110
8-digit binary of 46: 00101110
1's complement of -46: 11010001
2's complement of -46: 11010001 + 1
\( \implies \) 11010010
In simple words: To find the 1's complement, flip all the 0s to 1s and 1s to 0s in the binary form. To get the 2's complement, just add 1 to the 1's complement. This is how computers handle negative numbers internally.

🎯 Exam Tip: Always ensure you start with the 8-bit representation of the positive number before finding complements, and remember to add 1 to the LSB for the 2's complement.

 

Question 8.
a) \( 10_{10} + 15_{10} \)
b) \( -12_{10} + 5_{10} \)
c) \( 14_{10} - 12_{10} \)
d) \( (-2)_{10} - (-6)_{10} \)
Answer:
Binary arithmetic operations, like addition and subtraction, are fundamental in computer science. They follow specific rules for each bit position and handle carries or borrows, just like in decimal arithmetic. Converting numbers to binary before performing operations helps understand how computers process data.
a) \( 10_{10} + 15_{10} \)
Convert to binary:
For \( 10_{10} \):
\( 2 \lfloor 10 \) Remainder
\( 2 \lfloor 5 \)-0
\( 2 \lfloor 2 \)-1
\( 2 \lfloor 1 \)-0
\( 0 \)-1
So, \( 10_{10} = 1010_{2} \).
8-digit binary: 00001010

For \( 15_{10} \):
\( 2 \lfloor 15 \) Remainder
\( 2 \lfloor 7 \)-1
\( 2 \lfloor 3 \)-1
\( 2 \lfloor 1 \)-1
\( 0 \)-1
So, \( 15_{10} = 1111_{2} \).
8-digit binary: 00001111

Binary Addition:
00001010 \( (10_{10}) \)
+ 00001111 \( (15_{10}) \)
----------
00011001 \( (25_{10}) \)

Thus, \( 10_{10} + 15_{10} = 25_{10} \). In binary, \( 00001010_2 + 00001111_2 = 00011001_2 \).

b) \( -12_{10} + 5_{10} \)
First, convert \( 12_{10} \) and \( 5_{10} \) to binary and find 2's complement for \( -12_{10} \).
For \( 12_{10} \):
\( 2 \lfloor 12 \) Remainder
\( 2 \lfloor 6 \)-0
\( 2 \lfloor 3 \)-0
\( 2 \lfloor 1 \)-1
\( 0 \)-1
So, \( 12_{10} = 1100_{2} \).
8-digit binary for \( 12_{10} \): 00001100
1's complement of \( -12_{10} \): 11110011
2's complement of \( -12_{10} \): 11110011 + 1
\( \implies \) 11110100

For \( 5_{10} \):
\( 2 \lfloor 5 \) Remainder
\( 2 \lfloor 2 \)-1
\( 2 \lfloor 1 \)-0
\( 0 \)-1
So, \( 5_{10} = 101_{2} \).
8-digit binary for \( 5_{10} \): 00000101

Binary Addition \( -12_{10} + 5_{10} \):
11110100 \( (-12_{10} \text{ in 2's complement}) \)
+ 00000101 \( (5_{10}) \)
----------
11111001 \( (-7_{10} \text{ in 2's complement}) \)

The result \( 11111001_2 \) is the 2's complement of \( 7_{10} \), which means the sum is \( -7_{10} \).
\( -12_{10} + 5_{10} = -7_{10} \).

c) \( 14_{10} - 12_{10} \)
This can be written as \( 14_{10} + (-12)_{10} \).
For \( 14_{10} \):
\( 2 \lfloor 14 \) Remainder
\( 2 \lfloor 7 \)-0
\( 2 \lfloor 3 \)-1
\( 2 \lfloor 1 \)-1
\( 0 \)-1
So, \( 14_{10} = 1110_{2} \).
8-digit binary for \( 14_{10} \): 00001110

2's complement of \( -12_{10} \) (from part b): 11110100

Binary Addition \( 14_{10} + (-12)_{10} \):
00001110 \( (14_{10}) \)
+ 11110100 \( (-12_{10} \text{ in 2's complement}) \)
----------
\(1\)00000010
The carry digit is truncated. The result is 00000010.
Thus, \( 14_{10} - 12_{10} = 2_{10} \). In binary, \( 00001110_2 + 11110100_2 = 00000010_2 \).

d) \( (-2)_{10} - (-6)_{10} \)
This can be rewritten as \( (-2)_{10} + 6_{10} \).
For \( 2_{10} \): 00000010 (8-bit binary)
1's complement of \( -2_{10} \): 11111101
2's complement of \( -2_{10} \): 11111101 + 1
\( \implies \) 11111110

For \( 6_{10} \):
\( 2 \lfloor 6 \) Remainder
\( 2 \lfloor 3 \)-0
\( 2 \lfloor 1 \)-1
\( 0 \)-1
So, \( 6_{10} = 110_{2} \).
8-digit binary for \( 6_{10} \): 00000110

Binary Addition \( (-2)_{10} + 6_{10} \):
11111110 \( (-2_{10} \text{ in 2's complement}) \)
+ 00000110 \( (6_{10}) \)
----------
\(1\)00000100
The carry digit is truncated. The result is 00000100.
Thus, \( (-2)_{10} - (-6)_{10} = 4_{10} \). In binary, \( 11111110_2 + 00000110_2 = 00000100_2 \).
In simple words: To add or subtract binary numbers, especially with negative values, first convert all numbers to their binary form. For negative numbers, use the 2's complement. Then, perform binary addition, keeping track of any carries. If a carry goes beyond the number of bits (like 8-bit), ignore it for the final answer. This gives you the correct result.

🎯 Exam Tip: When performing binary subtraction using 2's complement, rewrite the subtraction as an addition (e.g., A - B becomes A + (-B)) and remember to discard any carry-out from the most significant bit in the final sum.