Simplify the following using K-Map. F(A, B,C,D) = ∑(3,4,5,6,7,11,15)
A’B+CD
In a 4-variable Karnaugh map, a group of four adjacent 1-cells (a quad) eliminates two variables. The aim is to cover every minterm with the fewest, largest groups; overlapping is allowed.
Step 1 — Minterms with A = 0, B = 1 are 4, 5, 6, 7. All four are present, forming a quad: A’B.
Step 2 — Minterms with C = 1, D = 1 are 3, 7, 11, 15. All four are present, forming a second quad (the CD column): CD. Minterm 7 is shared by both quads.
Step 3 — The two quads together cover {3, 4, 5, 6, 7, 11, 15}, exactly the given list, so F = A’B + CD.
AB+C’D covers 12–15 and 1, 5, 9, 13, missing 3, 4, 6, 7, 11; AC+BD covers 10, 11, 14, 15 and 5, 7, 13, 15, missing 3, 4, 6; A’B+B’C covers 4–7 and 2, 3, 10, 11, adding 2 and 10 and missing 15.
A’B+CD 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 ?
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 :
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 ?
