Discrete Mathematics Questions and Answers – Boolean Functions

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This set of Discrete Mathematics Multiple Choice Questions & Answers (MCQs) focuses on “Boolean Functions”.

1. What is the use of Boolean identities?
a) Minimizing the Boolean expression
b) Maximizing the Boolean expression
c) To evaluate a logical identity
d) Searching of an algebraic expression
View Answer

Answer: a
Explanation: Boolean identities are used for minimizing the Boolean expression and transforming into an equivalent expression.
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2. _________ is used to implement the Boolean functions.
a) Logical notations
b) Arithmetic logics
c) Logic gates
d) Expressions
View Answer

Answer: c
Explanation: To implement a Boolean function logic gates are used. Basic logic gates are AND, OR and NOT.

3. Inversion of single bit input to a single bit output using _________
a) NOT gate
b) NOR gate
c) AND gate
d) NAND gate
View Answer

Answer: a
Explanation: A NOT gate is used to invert a single bit input (say A) to a single bit of output (~A).

4. There are _________ numbers of Boolean functions of degree n.
a) n
b) 2(2*n)
c) n3
d) n(n*2)
View Answer

Answer: b
Explanation: There are 2n different n-tuples of 0’s and 1’s. A Boolean function is an assignment of 0’s or 1’s to each of these 2 n different n-tuples. Hence, there are 2(2*n) different Boolean functions.

5. A _________ is a Boolean variable.
a) Literal
b) String
c) Keyword
d) Identifier
View Answer

Answer: a
Explanation: A literal is a Boolean variable or its complement. A maxterm is a sum of n literals and a minterm is a product of n literals.
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6. Minimization of function F(A,B,C) = A*B*(B+C) is _________
a) AC
b) B+C
c) B`
d) AB
View Answer

Answer: d
Explanation: AB(B+C)
= ABB + ABC [Applying distributive rule]
= AB + ABC [Applying Idempotent law]
= AB (1+C)
= AB*1 [As, 1+C=1]
= AB.

7. The set for which the Boolean function is functionally complete is __________
a) {*, %, /}
b) {., +, -}
c) {^, +, -}
d) {%, +, *}
View Answer

Answer: b
Explanation: A Boolean function is represented by using three operators ., +, -. We can find a smaller set of functionally complete operators if one of the three operators of this set can be expressed in terms of the other two.

8. (X+Y`)(X+Z) can be represented by _____
a) (X+Y`Z)
b) (Y+X`)
c) XY`
d) (X+Z`)
View Answer

Answer: a
Explanation: (X+Y`) (X+Z)
= XX + XZ + XY`+ Y`Z
= X + XZ + XY`+ Y`Z
= X (1+Z) + XY`+ Y`Z
= X.1 + XY`+ Y`Z
= X (1+Y`) + Y`Z
= X + Y`Z.

9. __________ is a disjunctive normal form.
a) product-of-sums
b) product-of-subtractions
c) sum-of-products
d) sum-of-subtractions
View Answer

Answer: c
Explanation: The sum of minterms that represents the function is called the sum-of-products expansion or the disjunctive normal form. A Boolean sum of minterms has the value 1 when exactly one of the minterms in the sum has the value 1. It has the value 0 for all other combinations of values of the variables.
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10. a ⊕ b = ________
a) (a+b)(a`+b`)
b) (a+b`)
c) b`
d) a` + b`
View Answer

Answer: a
Explanation: a ⊕ b
= a`b + ab`
= a`b+aa` + bb` + ab` [As, a*a` = 0 and b*b` = 0]
= a`(a+b) + b`(a+b)
= (a+b)(a`+b`).

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Manish Bhojasia, a technology veteran with 20+ years @ Cisco & Wipro, is Founder and CTO at Sanfoundry. He is Linux Kernel Developer & SAN Architect and is passionate about competency developments in these areas. He lives in Bangalore and delivers focused training sessions to IT professionals in Linux Kernel, Linux Debugging, Linux Device Drivers, Linux Networking, Linux Storage, Advanced C Programming, SAN Storage Technologies, SCSI Internals & Storage Protocols such as iSCSI & Fiber Channel. Stay connected with him @ LinkedIn