# 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 1 Explanation:
 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 2 Explanation:
 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 3 Explanation:
 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 4 Explanation:
 Question 5
Minimum number of NAND gates required to implement the following binary equation$Y=(\bar{A}+\bar{B})(C+D)$
 A 4 B 5 C 3 D 6
ISRO CSE 2020   Digital Logic
Question 5 Explanation:
 Question 6
Consider the Boolean function $z(a,b,c)$. Which one of the following minterm lists represents the circuit given above?
 A $z=\Sigma (0,1,3,7)$ B $z=\Sigma (1,4,5,6,7)$ C $z=\Sigma (2,4,5,6,7)$ D $z=\Sigma (2,3,5)$
GATE CSE 2020   Digital Logic
Question 6 Explanation:
 Question 7
What is the minimum number of 2-input NOR gates required to implement 4-variable function expressed in sum-of-minterms from as $f = \Sigma (0, 2, 5, 7, 8, 10, 13, 15)$? Assume that all the inputs and their complements are available. Answer ________ .
 A 2 B 3 C 4 D 5
GATE CSE 2019   Digital Logic
Question 7 Explanation:
 Question 8
Consider three 4-variable functions $f_1,f_2 \; and \; f_3$, which are expressed in sum-of-minterms

$f_1=\Sigma (0,2,5,8,14)$
$f_2=\Sigma (2,3,6,8,14,15)$
$f_3=\Sigma (2,7,11,14)$

For the following circuit with one AND gate and one XOR gate, the output function f can be expressed as: A $\Sigma (7,8,11)$ B $\Sigma (2,7,8,11,14)$ C $\Sigma (2,14)$ D $\Sigma (0,2,3,5,6,7,8,11,14,15)$
GATE CSE 2019   Digital Logic
Question 8 Explanation:
 Question 9
Which one of the following is NOT a valid identity?
 A $(x\oplus y)\oplus z=x\oplus (y\oplus z)$ B $(x+ y)\oplus z=x\oplus (y+z)$ C $x\oplus y=x+y, \; if \; xy=0$ D $x\oplus y=(xy+x'y')'$
GATE CSE 2019   Digital Logic
Question 9 Explanation:
 Question 10
Any set of Boolean operation that is sufficient to represent all Boolean expression is said to be complete. Which of the following is not complete ?
 A {AND, OR} B {AND, NOT} C {NOT, OR} D {NOR}
ISRO CSE 2018   Digital Logic
Question 10 Explanation:

There are 10 questions to complete.

### 12 thoughts on “Boolean Algebra”

1. IN Q37 THERE IS AN ERROR IN QUESTION STATEMENT …

• We have updated the question.

2. Q62 OPTION (A) IS CORRECT PLS CORRECT IT ….

• 3. question no 83 ,

• Thank You Shivam,
We have updated the option.

4. q-2
opt (d) xyz whole bar is not correct. its x bar, y bar, z bar

• Thank You Ramananda Samantaray,
We have updated the option.

5. Check solution of question number 104 correct option is displayed wrong please rectify it. 👍

• Thank You PRAFUL SAMBHAJI RANE,

6. •  