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

GATE · 2025 · CS · Set 1 · Computer Science & IT

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

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

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 $F$ ?

A.
$\bar{b}_1 \bar{b}_0 + \bar{b}_2 \bar{b}_0 + b_1 \bar{b}_2 b_3$
B.
$\bar{b}_1 \bar{b}_0 + \bar{b}_2 \bar{b}_0$
C.
$\bar{b}_2 \bar{b}_0 + b_1 b_2 b_3$
D.
$\bar{b}_0 \bar{b}_2 + \bar{b}_3$

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