Consider a Boolean function f(w, x, y, z) such that aligned f(w, 0, 0, z) &= 1 \\ f(1, x, 1, z) &= x + z \\ f(w, 1, y, z) &= wz + y aligned The number of literals in the minimal sum-of-products expression of f is ________.

GATE CSE 2021 Set 2 Q62: Literals in the minimal SOP of a partially specified f(w,x,y,z)

Consider a Boolean function $f(w, x, y, z)$ such that

$\begin{aligned} f(w, 0, 0, z) &= 1 \\ f(1, x, 1, z) &= x + z \\ f(w, 1, y, z) &= wz + y \end{aligned}$

The number of literals in the minimal sum-of-products expression of $f$ is ________.

Try it: numerical answer: type the value

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Numerical answer. No negative marking.

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Answer: 6 (official GATE 2021 final answer key)

Concept used: Fill a 4-variable K-map from the three partial definitions, then find a minimal cover.

First step: Mark the cells: $x=0, y=0$ gives four 1s; $w=1, y=1$ gives 1 unless $x = z = 0$ ; $x=1$ gives 1 when $y=1$ or $wz=1$ .

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Source: official GATE 2021 Set 2 CS question paper and final answer key, organised by IIT Bombay. Question paper · Answer key