‹ Back to the paper
Reduce the above expression by using 4-variable Karnaugh map, showing the various groups (i.e…
Reduce the above expression $X(E, R, S, C)$ by using 4-variable Karnaugh map, showing the various groups (i.e. octal, quads and pairs).
Draw the logic gate diagram for the reduced expression. Assume that the variables and their complements are available as inputs.
Answer
Answer
Official answer key4-variable K-map for $X(E,R,S,C)=\Sigma(1,3,4,6,9,10,11,14,15)$ (rows in order E'R', E'R, ER, ER'; columns in order S'C', S'C, SC, SC' - Gray code order):
Groups formed:
Quad 1: cells (1,3,9,11) -> $R'C$
Quad 2: cells (10,11,14,15) -> $ES$
Pair: cells (4,6) -> $E'RC'$
Reduced SOP expression:
$X(E,R,S,C) = R'C + ES + E'RC'$
Logic gate diagram for X = R'C + ES + E'RC': three AND gates feeding one OR gate. AND gate 1 (2-input) has inputs R' and C, giving output R'C. AND gate 2 (2-input) has inputs E and S, giving output ES. AND gate 3 (3-input) has inputs E', R and C', giving output E'RC'. The three AND-gate outputs (R'C, ES, E'RC') are wired into the three inputs of a 3-input OR gate, whose output is labelled X(E,R,S,C) = R'C + ES + E'RC'.
From ISC 2025 Specimen Computer Science Paper 1, question 3(ii).