Computer Science
Convert the following cardinal expression into its canonical form and reduce it using Boolean laws:
F(L, M, O, P) = π(0, 2, 8, 10)
Boolean Algebra
ICSE
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Answer
Binary of 0 is 0000: L+M+O+P
Binary of 2 is 0010: L+M+O'+P Binary of 8 is 1000: L'+M+O+P
Binary of 10 is 1010: L'+M+O'+P
Canonical form:
(L+M+O+P).(L+M+O'+P).(L'+M+O+P).(L'+M+O'+P)
Reducing the expression using boolean laws:
(L+M+O+P).(L+M+O'+P).(L'+M+O+P).(L'+M+O'+P)
= (L+M+O+P).(L'+M+O+P).(L+M+O'+P).(L'+M+O'+P) [Associative Law]
= [(M+O+P) + (LL')].[(M+O'+P) + (LL')] [Distributive Law]
= [(M+O+P) + 0].[(M+O'+P) + 0] [Complementary Law]
= (M+O+P).(M+O'+P) [∵ a+0=a]
= (M+P) + (O.O') [Distributive Law]
= M+P+0 [Complementary Law]
= M+P [∵ a+0=a]
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