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

Explanation: Boolean identities are used for minimizing the Boolean expression and transforming into an equivalent expression.

2. _________ is used to implement the Boolean functions.

a) Logical notations

b) Arithmetic logics

c) Logic gates

d) Expressions

View Answer

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

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) n^{3}

d) n^{(n*2)}

View Answer

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

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.

6. Minimization of function F(A,B,C) = A*B*(B+C) is _________

a) AC

b) B+C

c) B`

d) AB

View Answer

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

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

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

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.

10. a ⊕ b = _____

a) (a+b)(a`+b`)

b) (a+b`)

c) b`

d) a` + b`

View Answer

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`).

**Sanfoundry Global Education & Learning Series – Discrete Mathematics.**

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