GATE ECE 2024 | Boolean Algebra Question 1 | Digital Circuits

GATE ECE 2024

MCQ (Single Correct Answer)

-0.33

For the Boolean function

$F(A, B, C, D) = \sum m(0,2,5,7,8,10,12,13,14,15)$,

the essential prime implicants are _________.

$BD$, $\overline{B}~\overline{D}$

$BD$, $AB$

$AB$, $\overline{B}~\overline{D}$

$BD$, $\overline{B}~\overline{D}$, $AB$

GATE ECE 2022

MCQ (More than One Correct Answer)

-0

Select the Boolean function(s) equivalent to x + yz, where x, y, and z are Boolean variables, and + denotes logical OR operation.

x + z + xy

(x + y) (x + z)

x + xy + yz

x + xz + xy

GATE ECE 2018

MCQ (Single Correct Answer)

-0.33

A function F(A, B, C) defined by three Boolean variables A, B and C when expressed as sum of products is given by

F = $$\overline A .\overline B .\overline C + \overline A .B.\overline C + A.\overline B .\overline C $$

where, $$\overline A $$, $$\overline B $$, and $$\overline C $$ are the complements of the respective variables. The product of sums (POS) form of the function F is

F = (A + B + C)(A + $$\overline B $$ + C)($$\overline A $$ + B + C)

F = ($$\overline A $$ + $$\overline B $$ + $$\overline C $$)($$\overline A $$ + B + $$\overline C $$)(A + $$\overline B $$ + $$\overline C $$)

F = (A + B + $$\overline C $$)(A + $$\overline B $$ + $$\overline C $$)($$\overline A $$ + B + $$\overline C $$)($$\overline A $$ + $$\overline B $$ + C)($$\overline A $$ + $$\overline B $$ + $$\overline C $$)

F = ($$\overline A $$ + $$\overline B $$ + C)($$\overline A $$ + B + C)(A + $$\overline B $$ + C)(A + B + $$\overline C $$)(A + B + C)

GATE ECE 2014 Set 1

MCQ (Single Correct Answer)

-0.3

The Boolean expression (X+Y)(X+$$\overline Y $$)+($$\overline {(X\overline Y ) + \overline X } $$ simplifies to