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Convert the following cardinal expression to its canonical form:

Computer Science20232 marksOne word
Convert the following cardinal expression to its canonical form: $F(P, Q, R) = \pi(0, 1, 3, 4)$

Answer

Answer

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$F(P, Q, R) = \pi(0, 1, 3, 4)$: 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: $F(P, Q, R) = (P + Q + R) \cdot (P + Q + R') \cdot (P + Q' + R') \cdot (P' + Q + R)$
Boolean Algebra

From ISC 2023 Computer Science Paper 1, question 5(iii).