# 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

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

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’

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

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

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.
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6. DeMorgan’s theorem states that _________
a) (AB)’ = A’ + B’
b) (A + B)’ = A’ * B
c) A’ + B’ = A’B’
d) (AB)’ = A’ + B

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’

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’)

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

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

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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