Out the following steps in the proper sequence for simplifying a Boolean function using a Karnaugh map (K-map). (A) Identify and group the largest possible cluster of 1’s (B) Draw the K-map for the given Boolean function (C) Write the simplified Boolean expression from the grouped clusters (D) Transfer the truth table values to the K-map Choose the correct answer from the options given below :
(B), (D), (A), (C)
A Karnaugh map is a grid arrangement of the truth table in Gray-code order, so that adjacent cells differ in one variable and groups of 1s can be read off as simplified product terms.
Step 1 — Draw the K-map (B): choose a grid with 2n cells for n variables and label rows and columns in Gray code.
Step 2 — Transfer the truth table values to the K-map (D): place a 1 in every cell whose minterm makes the function true.
Step 3 — Identify and group the largest possible clusters of 1s (A): groups of size 1, 2, 4, 8 …, as large and as few as possible, wrapping around the edges.
Step 4 — Write the simplified expression (C): each group contributes one product term containing only the variables that stay constant over the group.
Values cannot be transferred before the map is drawn, and grouping cannot happen before the 1s are placed, so the orders starting with transfer, grouping or placing grouping ahead of transfer are not workable.
(B), (D), (A), (C) option is correct.
Similar Questions
Consider the following statements :
(a) Boolean expressions and logic networks correspond to labelled acyclic digraphs.
(b) Optimal boolean expressions may not correspond to simplest networks.
(c) Choosing essential blocks first in a Karnaugh map and then greedily choosing the largest remaining blocks to cover may not give an optimal expression.
Which of these statement(s) is/are correct ?
Simplify the following using K-Map.
F(A, B,C,D) = ∑(3,4,5,6,7,11,15)
Which of the following is the simplified form of the given function.
f(A,B,C)=∑m(0,1,3,7)
Important Questions from Minimization of Boolean Expression
Simplify the following Boolean expression.
E(E + F) + DE + D(E + F)
What is the value of \( \bar{F}\)?
\(F = AB + \bar{C}\bar{D} + \bar{B}D\)
Which statement(s) is/are correct regarding the Boolean algebra?
I. It facilitate the analysis and design of digital circuits.
II. Expresses in algebraic form the input-output relationship of logic diagram.
The input-output relationship of the binary variable for each gate can be represented in tabular form by a _______.
Which of the following statements about the K-maps is INCORRECT ?
