CBSE Class 7 Computer Science Number System Worksheet Set 01

Answer: A computer is built from electronic circuits that have only two states, on and off. These two states are easily represented by the two binary digits 1 and 0, which makes the system fast and reliable.

Teacher's Note:
1. Two states are much easier to build and detect than ten.
2. This is why binary suits hardware.

Answer: Long binary numbers are hard for people to read and write. Octal and hexadecimal give a short form, because one octal digit stands for 3 bits and one hexadecimal digit stands for 4 bits.

Teacher's Note:
1. They are only shorthand for binary.
2. The computer itself still works in binary.

Answer: Decimal has base 10, binary base 2, octal base 8 and hexadecimal base 16.

Teacher's Note:
1. The base equals the number of digits used in the system.
2. Hexadecimal needs 16 symbols.

Answer: In a number system the value of a digit depends on its position. A digit is multiplied by a power of the base according to its place, so 2 in 20 and 2 in 200 have different values.

Teacher's Note:
1. Without place value, 21 and 12 would look alike.
2. Position gives each digit its weight.

Answer: Decimal value = sum of (digit × base^position), where positions are counted from the right starting at 0.
Example: 101 in binary = 1×2² + 0×2¹ + 1×2⁰ = 5.

Teacher's Note:
1. Always begin counting positions from 0 on the right.
2. Add all the products at the end.

Answer: The decimal, binary, octal and hexadecimal number systems.

Teacher's Note:
1. There are four of them.
2. Decimal is used by people; the other three are used with computers.

Answer: 1011 = 1×8 + 0×4 + 1×2 + 1×1 = 8 + 0 + 2 + 1 = 11.

Teacher's Note:
1. Write the powers of 2 under each digit.
2. Add only where the digit is 1.

Answer: Divide by 2 repeatedly: 13 ÷ 2 = 6 r 1; 6 ÷ 2 = 3 r 0; 3 ÷ 2 = 1 r 1; 1 ÷ 2 = 0 r 1.
Reading the remainders from bottom to top: 1101.

Teacher's Note:
1. The last remainder is the leftmost digit.
2. Check by converting back: 8 + 4 + 1 = 13.

Answer: 10 = A, 11 = B, 12 = C, 13 = D, 14 = E and 15 = F.

Teacher's Note:
1. Hexadecimal needs six extra symbols after 9.
2. These are the letters A to F.

Answer: binary. Binary means based on two.

Teacher's Note:
1. These digits are called bits.
2. Everything in a computer is stored with them.

Answer: byte. 1 byte = 8 bits.

Teacher's Note:
1. The byte is the basic unit for measuring memory.
2. Kilobytes and megabytes are built from it.

Answer: 0 to 255. Eight bits give 2⁸ = 256 different values.

Teacher's Note:
1. Count starts at 0, so the largest value is 255.
2. All eight bits as 1 give 255.

Answer: bit (binary digit). It is the smallest unit of data.

Teacher's Note:
1. A bit is either off (0) or on (1).
2. Eight bits form a byte.

Answer: power. For example, in decimal the places are 10⁰, 10¹, 10² and so on.

Teacher's Note:
1. The power increases by one for each place to the left.
2. This gives units, tens, hundreds.

Answer: False. Computers work in binary.

Teacher's Note:
1. Decimal numbers are converted to binary before processing.
2. We see decimal only on screen.

Answer: True. 8 bits = 1 byte.

Teacher's Note:
1. This is a basic fact of computer memory.
2. Learn it with 1 nibble = 4 bits.

Answer: True. Each place has its own weight, a power of the base.

Teacher's Note:
1. The same digit means different values in different places.
2. That is place value.

Answer: False. There are four common systems: decimal, binary, octal and hexadecimal.

Teacher's Note:
1. Do not add any other system to the list.
2. Learn the four with their bases.

Answer: True. Memory, addresses and colours are all expressed with these systems.

Teacher's Note:
1. Hexadecimal appears in colour codes on web pages.
2. Binary is behind all storage.

Answer: (a) binary. Binary uses 0 and 1.

Teacher's Note:
1. Two digits match the on/off states of electronic circuits.
2. That is why binary is basic.

Answer: (a) Octal, hexadecimal. Octal and hexadecimal are compact forms of binary.

Teacher's Note:
1. Both groups of bits convert directly to a single digit.
2. Decimal does not map neatly to binary.

Answer: (b) 10. Decimal uses ten digits, 0 to 9.

Teacher's Note:
1. The base is the count of distinct digits.
2. Our everyday system is base 10.

Answer: (c) F. 15 is the last single hexadecimal digit, F.

Teacher's Note:
1. The digits go 0 to 9 and then A to F.
2. So A = 10 and F = 15.

Answer: (c) 4. One hexadecimal digit represents exactly 4 bits.

Teacher's Note:
1. For example, 1111 = F.
2. Octal groups bits in threes.