**Digital Circuits Questions and Answers – Boolean Logic Operations**

This set of Digital Electronics/Circuits Multiple Choice Questions & Answers (MCQs) focuses on “Boolean Logic Operations”.

**1. In boolean algebra, the OR operation is performed by which properties?**

a) Associative properties

b) Commutative properties

c) Distributive properties

d) All of the Mentioned

**Answer:**d

**Explanation:**The expression for Associative property is given by A+(B+C) = (A+B)+C & A*(B*C) = (A*B)*C.

The expression for Commutative property is given by A+B = B+A & A*B = B*A.

The expression for Distributive property is given by A+BC=(A+B)(A+C) & A(B+C) = AB+AC.

**2. The expression for Absorption law is given by _________**

a) A + AB = A

b) A + AB = B

c) AB + AA’ = A

d) A + B = B + A

**Answer:**a

**Explanation:**The expression for Absorption Law is given by: A+AB = A.

Proof: A + AB = A(1+B) = A (Since 1 + B = 1 as per 1’s Property).

**3. According to boolean law: A + 1 = ?**

a) 1

b) A

c) 0

d) A’

**Answer:**a

**Explanation:**A + 1 = 1, as per 1’s Property.

**4. The involution of A is equal to _________**

a) A

b) A’

c) 1

d) 0

**Answer:**a

**Explanation:**The involution of A means double inversion of A (i.e. A”) and is equal to A.

Proof: ((A)’)’ = A

**5. A(A + B) = ?**

a) AB

b) 1

c) (1 + AB)

d) A

**Answer:**d

**Explanation:**A(A + B) = AA + AB (By Distributive Property) = A + AB (A.A = A By Commutative Property) = A(1 + B) = A*1 (1 + B = 1 by 1’s Property) = A.

**6. DeMorgan’s theorem states that _________**

a) (AB)’ = A’ + B’

b) (A + B)’ = A’ * B

c) A’ + B’ = A’B’

d) (AB)’ = A’ + B

**Answer:**a

**Explanation:**The DeMorgan’s law states that (AB)’ = A’ + B’ & (A + B)’ = A’ * B’, as per the Dual Property.

**7. (A + B)(A’ * B’) = ?**

a) 1

b) 0

c) AB

d) AB’

**Answer:**b

**Explanation:**The DeMorgan’s law states that (AB)’ = A’ + B’ & (A + B)’ = A’ * B’, as per the Dual Property.

**8. Complement of the expression A’B + CD’ is _________**

a) (A’ + B)(C’ + D)

b) (A + B’)(C’ + D)

c) (A’ + B)(C’ + D)

d) (A + B’)(C + D’)

**Answer:**b

**Explanation:**(A’B + CD’)’ = (A’B)'(CD’)’ (By DeMorgan’s Theorem) = (A” + B’)(C’ + D”) (By DeMorgan’s Theorem) = (A + B’)(C’ + D).

**9. Simplify Y = AB’ + (A’ + B)C.**

a) AB’ + C

b) AB + AC

c) A’B + AC’

d) AB + A

**Answer:**a

**Explanation:**Y = AB’ + (A’ + B)C = AB’ + (AB’)’C = (AB’ + C)( AB’ + AB’) = (AB’ + C).1 = (AB’ + C).

**10. The boolean function A + BC is a reduced form of ____________**

a) AB + BC

b) (A + B)(A + C)

c) A’B + AB’C

d) (A + C)B

**Answer:** b

**Explanation:** (A + B)(A + C) = AA + AC + AB + BC = A + AC + AB + BC (By Commutative Property) = A(1 + C + B) + BC = A + BC (1 + B + C =1 By 1’s Property).

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