CBSE Class 12 Computers Boolean Algebra Worksheet

1. State Demorgan’s laws. Verify one of the laws using truth table.

2. State and prove

a. Law of Duality. Give the dual of (A+BC+(AB)’).

b. Distributive Law

c. Idempotent Law

d. Absorption Law

3. Reduce the following Boolean expression:

a. H(U,V,W,Z) = Σ(0,1,4,5,6,7,11,12,13,14,15)

b. F(A,B,C,D) = π(5,6,7,8,9,12,13,14,15)

4. Verify the following algebraically:

a. X.Y’.Z+X.Y’.Z’+X’.Y’.Z = X.Y’+Y’

b. XY+YZ+Y’Z = XY+Z

c. XY+YZ+YZ’=Y

5. Draw a logic circuit diagram for the following Boolean expressions:

a. A.(B+C’)

b. X.Y’+Y.Z’ (using NAND gates only)

c. (A+B)(A+B’)

d. X(Y’+Z) (using NOR gate only)

6. Given the following truth table, derive the SOP and POS

7. A majority gate is a digital circuit whose output is 1 if the majority of inputs are 1’s. The output is 0 otherwise. By means of a truth table, find the Boolean function implemented by 3‐input majority gates.

8. Simplify using K‐map for:
a. F(w,x,y,z) = M₂ + M₃ + M₄ + M₅ + M₆ + M₇ + M₉ + M₁₁ + M₁₃ (M‐Maxterm, m‐Minterm
b. F(a,b,c,d) = π(₁,2,4,5,7,10,15)
c. F(w,x,y,z) = m₂ + m₃ + m₅ + m₆ + m₇ + m₉ + m₁₁ +m₁₃ (M‐Maxterm, m‐Minterm
d. F(a,b,c,d) = Σ(0,7,8,9,10)
e. y’t’ + y’z’ + yzt’ + yz’t’

9. Use the NAND gate to form
a. Two input OR gate
b. Two‐input AND gate
c. NOT gate

10. Use the NOR gate to form
a. Two input OR gate
b. Two‐input AND gate
c. NOT gate