# GATE Questions & Answers of Boolean Algebra

## What is the Weightage of Boolean Algebra in GATE Exam?

Total 16 Questions have been asked from Boolean Algebra topic of Digital Logic subject in previous GATE papers. Average marks 1.38.

Which one of the following is NOT a valid identity?

Let $\style{font-family:'Times New Roman'}\oplus$ and $\style{font-family:'Times New Roman'}\odot$ denote the Exclusive OR and Exclusive NOR operations, respectively.

Which one of the following is NOT CORRECT?

Consider the minterm list form of a Boolean function F given below.

$\style{font-family:'Times New Roman'}{F\left(P,Q,R,S\right)=\sum m\left(0,2,5,7,9,11\right)+d\left(3,8,10,12,14\right)}$

Here, m denotes a minterm and d denotes a don’t care term. The number of essential prime implicants of the function F is ______.

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

Consider the Boolean operator # with the following properties:

$x\#0\;=\;x,\;x\#1\;=\;\overline x,\;x\#x\;=\;0\;and\;x\#\overline x\;=1.$ Then $x#y$ is equivalent to

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 ________.

The binary operator $\ne$ is defined by the following truth table.

 p q p$\ne$q 0 0 0 0 1 1 1 0 1 1 1 0

Which one of the following is true about the binary operator $\ne$?

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

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

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

$\left(P+\overline{)Q}+\overline{)R}\right).\left(P+\overline{)Q}+R\right).\left(P+Q+\overline{)R}\right)$ is

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?

Given f1, f3 and f in canonical sum of products form (in decimal) for the circuit f1 = ${\sum }_{}$m (4, 5, 6, 7, 8)
f3 = ${\sum }_{}$m (1, 6, 15)
f = ${\sum }_{}$m (1, 6, 8, 15)
then f2 is

If P, Q, R are Boolean variables, then

$\left(P+\overline{Q}\right)\left(P.\overline{Q}+P.R\right)\left(\overline{P}.\overline{R}+\overline{Q}\right)$

Simplifies to

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

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?

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:

${P}_{i}={A}_{i}\oplus {B}_{i}$ and ${G}_{i}={A}_{i}{B}_{i}$

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

${S}_{i}={P}_{i}\oplus {C}_{i}$ and ${C}_{i+1}={G}_{i}+{P}_{i}{C}_{i}$ ,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: