GATE ECE 2026 | Boolean Algebra Question 1 | Digital Circuits

GATE ECE 2026

MCQ (More than One Correct Answer)

-0.67

Consider the four-variable Boolean function, $f(w, x, y, z)=\Sigma m(0,2,5,7,8,10,13,14,15)$ with ' $w$ ' as MSB and ' $z$ ' as LSB. Which of the following expressions is/are the valid form(s) of $f(w, x, y, z)$ ?

$\bar{x} \bar{z}+x z+w x y$

$x z+w x y+w \bar{x} \bar{z}+\bar{w} x y \bar{z}$

$\bar{x} \bar{z}+w x y+w \bar{x} \bar{z}+\bar{w} x y \bar{z}$

$\bar{x} \bar{z}+x z+w y \bar{z}$

GATE ECE 2017 Set 1

MCQ (Single Correct Answer)

-0.6

Which one of the following gives the simplified sum of products expression for the Boolean function $$F = {m_0} + {m_2} + {m_3} + {m_5},$$ where $$F = {m_0} + {m_2} + {m_3} + {m_5},$$ are minterms corresponding to the inputs A, B and C with A as the MSB and C as the LSB?

$$\overline A B + \,\overline A \,\overline B \,\overline C + \,A\overline B \,C$$

$$\overline A \,\overline C + \overline A B + A\overline B C$$

$$\overline A \,\overline C + A\,\overline B + A\overline B C$$

$$\overline A \,BC + \overline A \,\overline C + A\,\overline B C$$

GATE ECE 2016 Set 3

MCQ (Single Correct Answer)

-0.6

Following is the k-map of a Boolean function of five variable P, Q, R, S and X. The minimum for the function is GATE ECE 2016 Set 3 Digital Circuits - Boolean Algebra Question 11 English

GATE ECE 2016 Set 3 Digital Circuits - Boolean Algebra Question 11 English

$$\overline P \,\overline {Q\,} \,S\overline X + P\overline Q \,S\overline X + Q\,\overline R \,\,\overline S X + QR\overline {S\,} X$$

$$\overline {Q\,} \,S\,\overline X \, + Q\,\overline S \,X$$

$$\overline {Q\,} S\,X + Q\,\overline S \,\overline X $$

$$\overline {Q\,} S\, + Q\,\overline S \,$$

GATE ECE 2015 Set 1

MCQ (Single Correct Answer)

-0.6

The Boolean expression F(X, Y, Z)= $$\overline X Y\overline Z + X\overline {Y\,} \overline Z + XY\overline Z + XYZ$$ converted into the canonical product of sum (POS)from is

$$(x + y + z)(x + y + \overline z )(x + \overline y + \overline z )(\overline x + y + \overline z )$$

$$(x + \overline y + z)(\overline x + y + \overline z )(\overline x + \overline y + z)(\overline x + \overline y + z)$$

$$(x + y + z)(\overline x + y + \overline z )(x + \overline y + z)(\overline x + \overline y + \overline z )$$

$$(x + \overline y + \overline z )(\overline x + y + z)(\overline x + \overline y + z)(x + y + z)$$