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# Unit_7 - Unit 7 Problem Solutions 7.1(a f cd ab 00 00 01 11...

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Unit 7 Problem Solutions a b c d 00 01 11 10 00 01 11 10 0 0 0 0 1 0 1 1 1 1 1 0 0 0 0 0 f = (a'+ b') (a + b ) (a + c + d') (b + c'+ d') f = (a'+ b') (a + b ) (b + c'+ d') (b'+ c + d') f = (a'+ b') (a + b ) (a + c + d') (a'+ c'+ d') f = (a'+ b') (a + b ) (b'+ c + d') (a'+ c'+ d') a b c d 00 01 11 10 00 01 11 10 0 0 0 0 1 0 1 1 1 1 1 0 0 0 0 0 f = a b'd' + a b'c' + a'b c + a'b d' f = a'b (c + d') + ab' (c' + d') 2 2 2 3 3 7.1 (a) Sum of products solution requires 5 gates, 16 inputs Beginning with a minimum product of sums solution, we can get Beginning with the minimum sum of products solution, we can get F = (A + B + D') [(B + D) + A'E'] (C' + E') 2 2 3 3 3 F = (E + FG) [A + B (C + D)] 2 2 2 2 2 2 7.1 (b) AC'D + ADE' + BE' + BC' + A'D'E' = E' (AD + B) + A'D'E' + C' (AD + B) = (AD + B) (E' + C') + A'D'E' = (A + B +D') (A+ B + E') (A' + B +D) (B + D + E') (C' + E') = (A + B +D') [(B + D) + A'E'] (C' + E') 7.2 (a) 3 levels, 5 gates, 13 inputs 7.2 (b) AE + BDE + BCE + BCFG + BDFG + AFG = AE + AFG + BE (C + D) + BFG (C + D) 4 levels, 6 gates, 12 inputs Product of sums solution requires 5 gates, 14 inputs, so product of sums solution is minimum. 5 gates, 12 inputs f = (a + b) (a' + b') (d' + ac' + a'c)) 2 2 2 2 3 3 6 gates, 14 inputs So sum of products solution is minimum.

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a' c' a b d' F NOR-NOR d' a c a' b' F AND-NOR NAND-AND d a c a' b' F OR-AND a' c' a b d F A B C D 00 01 11 10 00 01 11 10 0 0 0 0 0 1 0 1 0 1 0 0 0 1 0 0
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