GATE CS 2026 Set 2 — Question 40
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Digital Logic → Boolean Algebra & Logic Gates → K-Map Minimization
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Question
Consider the following 4-variable Boolean functionConsider as MSB, as LSB. Which one of the following options represents the minimal sum of products form for the above function?Note: is OR operation, is AND operation, is NOT operation
Correct answer
(B) B'
Solution
The minterms are given as .
Let's map these to a 4-variable K-map ( as rows, as columns).Row (Indices 0, 1, 2, 3): All are 1s. This corresponds to the term .
Row (Indices 4, 5, 6, 7): All are 0s.
Row (Indices 12, 13, 14, 15): All are 0s.
Row (Indices 8, 9, 10, 11): All are 1s. This corresponds to the term .Combining the two groups of 1s:
Alternatively, looking at the binary representations:
0, 1, 2, 3: 0000, 0001, 0010, 0011 (independent of C, D)
8, 9, 10, 11: 1000, 1001, 1010, 1011 (independent of C, D)In both cases, must be 0. can be 0 or 1. and can be anything.
Thus, the function is .
Let's map these to a 4-variable K-map ( as rows, as columns).Row (Indices 0, 1, 2, 3): All are 1s. This corresponds to the term .
Row (Indices 4, 5, 6, 7): All are 0s.
Row (Indices 12, 13, 14, 15): All are 0s.
Row (Indices 8, 9, 10, 11): All are 1s. This corresponds to the term .Combining the two groups of 1s:
Alternatively, looking at the binary representations:
0, 1, 2, 3: 0000, 0001, 0010, 0011 (independent of C, D)
8, 9, 10, 11: 1000, 1001, 1010, 1011 (independent of C, D)In both cases, must be 0. can be 0 or 1. and can be anything.
Thus, the function is .
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