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Write the canonical form of the cardinal terms, and for .

Computer Science20242 marksOne word
Write the canonical form of the cardinal terms, $m_3$ and $M_5$ for $F (A, B, C, D)$.

Answer

Answer

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For F(A,B,C,D) (4 variables), an uncomplemented variable in a minterm corresponds to bit 1 and a complemented variable corresponds to bit 0 (minterm index read directly as the binary value ABCD); for a maxterm the convention is reversed - an uncomplemented variable corresponds to bit 0 and a complemented variable corresponds to bit 1. $m_3$: 3 = 0011 in binary (A B C D), so A=0, B=0, C=1, D=1: $m_3 = A'B'CD$ $M_5$: 5 = 0101 in binary (A B C D), so A=0, B=1, C=0, D=1 (bit 1 -> complemented literal, bit 0 -> uncomplemented literal): $M_5 = A + B' + C + D'$
Boolean Algebra

From ISC 2024 Computer Science Paper 1, question 5(iii).