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Consider the following four-variable Boolean function in sum-of-products form: F(b3, b2, b1, b0) = a3(0, 2, 4, 8, 10, 11, 12). Here, the value of the function is computed by considering b3b2b1b0 as a 4-bit binary number, where b3 denotes the most significant bit and b0 denotes the least significant bit. There are no don't-care terms. Which ONE of the following options is the correct minimized Boolean expression for F?

1. b4b1 b4b0 + b4b2 b4b0 + b1 b4b2 b4b3
2. b4b1 b4b0 + b4b2 b4b0
3. b4b2 b4b0 + b1 b2 b3
4. b4b0 b4b2 + b4b3

Correct answer: b4b1 b4b0 + b4b2 b4b0 + b1 b4b2 b4b3

Solution

The minterms 0, 2, 8, 10 form a group giving b4b1b4b0. The minterms 0, 4, 8, 12 form another group giving b4b2b4b0. The remaining minterm 11 is covered by b1b4b2b4b3, so the minimized expression is the sum of these terms.

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