Discrete Mathematics Questions and Answers – Boolean Functions

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

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

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

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)

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

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

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) {%, +, *}

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`)

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

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`

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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