Which of the following is the simplified form of the given function. f(A,B,C)=∑m(0,1,3,7)
A'B'+BC
A sum-of-minterms function is simplified by grouping adjacent minterms (those differing in one variable) on a Karnaugh map, which removes the variable that changes.
Step 1 — Write the minterms in binary (A B C): m0 = 000 = A'B'C', m1 = 001 = A'B'C, m3 = 011 = A'BC, m7 = 111 = ABC.
Step 2 — Pair m0 and m1: A'B'C' + A'B'C = A'B'(C' + C) = A'B'.
Step 3 — Pair m3 and m7: A'BC + ABC = BC(A' + A) = BC.
Step 4 — The two groups already cover all four minterms (m1 and m3 could also pair into A'C, but that group is redundant), so the minimal sum of products is f = A'B' + BC.
A'B'C'+A'B'C+A'BC+ABC is only the canonical (unsimplified) form, and A'B'+A'BC+ABC is equal to the function but still contains a removable literal pair. A'B'+BC' covers minterms 0, 1, 2 and 6, which is a different function.
A'B'+BC 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)
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 :
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 ?
