Skip to content
GATETECH
Official PYQ · 2025Set 2 · Q33Minimization (K-Maps etc.)MSQ2 marks

GATE CS 2025 Set 2 Q33 — Minimization (K-Maps etc.)

Explain with AI

​​​​Given the following Karnaugh Map for a Boolean function F(w,x,y,z)F(w, x, y, z) :

K Map


Which one or more of the following Boolean expression(s) represent(s) FF ?

Select all correct options
View worked solution

Answer: A;D

To find which expressions represent the Boolean function F(w,x,y,z)F(w, x, y, z), we can simplify the given options and compare them.

1. Simplifying Option A:

FA=wˉxˉyˉzˉ+wxˉyˉzˉ+wˉxˉyzˉ+wxˉyzˉ+xz=xˉyˉzˉ(wˉ+w)+xˉyzˉ(wˉ+w)+xz=xˉyˉzˉ+xˉyzˉ+xz=xˉzˉ(yˉ+y)+xz=xˉzˉ+xz\begin{aligned} F_A &= \bar{w} \bar{x} \bar{y} \bar{z} + w \bar{x} \bar{y} \bar{z} + \bar{w} \bar{x} y \bar{z} + w \bar{x} y \bar{z} + x z \\ &= \bar{x} \bar{y} \bar{z} (\bar{w} + w) + \bar{x} y \bar{z} (\bar{w} + w) + x z \\ &= \bar{x} \bar{y} \bar{z} + \bar{x} y \bar{z} + x z \\ &= \bar{x} \bar{z} (\bar{y} + y) + x z \\ &= \bar{x} \bar{z} + x z \end{aligned}

This matches Option D exactly. Thus, both Option A and Option D represent the same function F=xˉzˉ+xzF = \bar{x} \bar{z} + x z.

2. Verifying Options B and C:

  • Option B: Contains wxˉyzw \bar{x} y z (minterm m11m_{11}), which is not present in FF.
  • Option C: Contains wxˉyˉzw \bar{x} \bar{y} z (minterm m9m_9), which is not present in FF.

Therefore, only expressions A and D represent the function FF.

Free practice · Your answers on this page are not saved.

Published
Report a correction
Keep exploringMore Minimization (K-Maps etc.) questions