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
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.
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.
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 _________
= ABB + ABC [Applying distributive rule]
= AB + ABC [Applying Idempotent law]
= AB (1+C)
= AB*1 [As, 1+C=1]
7. The set for which the Boolean function is functionally complete is __________
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 _____
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.
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 = _____
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)
Sanfoundry Global Education & Learning Series – Discrete Mathematics.
To practice all areas of Discrete Mathematics, here is complete set of 1000+ Multiple Choice Questions and Answers.