Questions & Answers of Boolean Algebra

Question No. 127

If w, x, y, z are Boolean variables, then which one of the following is INCORRECT ?

Question No. 16

Consider the Boolean operator # with the following properties:

x#0 = x, x#1 =x, x#x = 0 and x#x = 1. Then x#y is equivalent to

Question No. 119

Let X be the number of distinct 16-bit integers in 2's complement representation. Let Y be the number of distinct 16-bit integers in sign magnitude representation. Then X-Y is ________.

Question No. 40

The binary operator is defined by the following truth table.

p q pq
0 0 0
0 1 1
1 0 1
1 1 0
Which one of the following is true about the binary operator ?

Question No. 21

Which one of the following expressions does NOT represent exclusive NOR of x and y?

Question No. 13

Which one of the following circuits is NOT equivalent to a 2-input XNOR (exclusive NOR) gate?

Question No. 14

The simplified SOP (Sum of Product) form of the Boolean expression

P+Q+R.P+Q+R.P+Q+R is

Question No. 6

What is the minimum number of gates required to implement the Boolean function (AB+C) if we have to use only 2-input NOR gates?

Question No. 8

Given f1, f3 and f in canonical sum of products form (in decimal) for the circuit

f1 = m (4, 5, 6, 7, 8)
f3 = m (1, 6, 15)
f = m (1, 6, 8, 15)
then f2 is

Question No. 26

If P, Q, R are Boolean variables, then


Simplifies to

Question No. 3

What is the maximum number of different Boolean functions involving n Boolean variables?

Question No. 33

Define the connective * for the Boolean variables X and Y as: X * Y = XY + X'Y'. Let Z =X *Y. Consider the following expressions P,Q and R.

P: X = Y *Z   Q: Y = X *Z   R: X *Y *Z = 1

Which of the following is TRUE?

Question No. 35

In a look-ahead carry generator, the carry generate function Gi and the carry propagate function Pi for inputs Ai and Bi are given by:

Pi=AiBi and Gi=AiBi

The expressions for the sum bit Si and the carry bit Ci+1 of the look-ahead carry adder are given by:

Si=PiCi and Ci+1=Gi+PiCi ,where C0 is the input carry

Consider a two-level logic implementation of the look-ahead carry generator. Assume that all Pi and Gi are available for the carry generator circuit and that the AND and OR gates can have any number of inputs. The number of AND gates and OR gates needed to implement the look-ahead carry generator for a 4-bit adder with S3, S2, S1, S0, and C4 as its outputs are respectively: