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Convert the following cardinal expression to its canonical form:
Convert the following cardinal expression to its canonical form:
$F(P, Q, R) = \pi(0, 1, 3, 4)$
Answer
Answer
AI$F(P, Q, R) = \pi(0, 1, 3, 4)$: write each maxterm in binary; a 0 bit gives the variable as it is and a 1 bit gives its complement, and the variables within a term are added.
$0 = 000 \to (P + Q + R)$
$1 = 001 \to (P + Q + R')$
$3 = 011 \to (P + Q' + R')$
$4 = 100 \to (P' + Q + R)$
Canonical form: $F(P, Q, R) = (P + Q + R) \cdot (P + Q + R') \cdot (P + Q' + R') \cdot (P' + Q + R)$
From ISC 2023 Computer Science Paper 1, question 5(iii).