Boolean Algebra


Question 1
Consider a Boolean function f(w,x,y,z) such that

\begin{array}{lll} f(w,0,0,z) & = & 1 \\ f(1,x,1,z) & =& x+z \\ f(w,1,y,z) & = & wz +y \end{array}

The number of literals in the minimal sum-of-products expression of f is ________
A
4
B
6
C
8
D
9
GATE CSE 2021 SET-2   Digital Logic
Question 2
Consider the following Boolean expression.

F=(X+Y+Z)(\overline X +Y)(\overline Y +Z)

Which of the following Boolean expressions is/are equivalent to \overline F (complement of F)?
[MSQ]
A
(\overline X +\overline Y +\overline Z)(X+\overline Y)(Y+\overline Z)
B
X\overline Y + \overline Z
C
(X+\overline Z)(\overline Y +\overline Z)
D
X\overline Y +Y\overline Z + \bar X \bar Y \bar Z
GATE CSE 2021 SET-1   Digital Logic


Question 3
The following circuit compares two 2-bit binary numbers, X and Y represented by X_{1}X_{0} and Y_{1}Y_{0} respectively. (X_{0} and Y_{0} represent Least Significant Bits)

Under what conditions Z will be 1?
A
X > Y
B
X < Y
C
X=Y
D
X!=Y
ISRO CSE 2020   Digital Logic
Question 4
If ABCD is a 4-bit binary number, then what is the code generated by the following circuit?

A
BCD code
B
Gray code
C
8421 code
D
Excess-3 code
ISRO CSE 2020   Digital Logic
Question 5
Minimum number of NAND gates required to implement the following binary equationY=(\bar{A}+\bar{B})(C+D)
A
4
B
5
C
3
D
6
ISRO CSE 2020   Digital Logic




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