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GATE 2025 CS (CS1) – Question 42

Digital Logic · Boolean Algebra and Minimization · 2 marks · Multiple choice

Consider the following four variable Boolean function in sum-of-product form

$F(b_3,b_2,b_1,b_0) = \sum(0,2,4,8,10,11,12)$.

where the value of the function is computed by considering $b_3b_2b_1b_0$ as a 4-bit binary number, where $b_3$ denotes the most significant bit and $b_0$ denotes the least significant bit. Note that there are no don't care terms. Which ONE of the following options is the CORRECT minimized Boolean expression for $F$?

  1. $\bar b_1\bar b_0 + \bar b_2\bar b_0 + b_1\bar b_2 b_3$
  2. $\bar b_1\bar b_0 + \bar b_2\bar b_0$
  3. $\bar b_2\bar b_0 + b_1 b_2 b_3$
  4. $\bar b_0\bar b_2 + \bar b_3$

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Correct answer: (A) $\bar b_1\bar b_0 + \bar b_2\bar b_0 + b_1\bar b_2 b_3$

Explanation

b1'b0' covers minterms 0,4,8,12. b2'b0' covers 0,2,8,10. The remaining minterm 11 pairs with 10 as b3·b2'·b1. So F = b1'b0' + b2'b0' + b3b2'b1.