homework5_soln_2009_corrected - Homework#5Solutions...

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Homework #5 Solutions ECE 15A, Winter 2009 1) F(a,b,c,d) = Σm ( 2,3,4,5,6,7,9,12,15) + Σd(1, 10,13) Size 1 Implicants 1 1’s m1 m2 m4 0001 0010 0100 2 1’s m3 m5 m6 m9 m10 m12 0011 0101 0110 1001 1010 1100 3 1’s m7 m13 0111 1101 4 1’s m15 1111 Size 2 Implicants abcd F m0 0000 m1 0001 x m2 0010 1 m3 0011 1 m4 0100 1 m5 0101 1 m6 0110 1 m7 0111 1 m8 1000 m9 1001 1 m10 1010 x m11 1011 m12 1100 1 m13 1101 x m14 1110 m15 1111 1 1 1’s m(1, 3) m(1, 5) m(1, 9) m(2, 3) m(2, 6) m(2, 10) m(4, 5) m(4, 6) m(4, 12) 00‐1 0‐01 ‐001 001‐ 0‐10 ‐010 010‐ 01‐0 ‐100 2 1’s m(3, 7) m(5, 7) 0‐11 01‐1
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Size 4 implicants 1 1’s m(1, 3, 5, 7) m(1, 5, 9 13) m(2, 3, 6, 7) m(4, 5, 6, 7) m(4 , 5, 12, 13) 0‐‐1 ‐‐01 0‐1‐ 01‐‐ ‐10‐ 2 1’s m(5, 7, 13, 15) ‐1‐1 Prime Implicant Chart 2 3 4 5 6 7 9 12 15 m(1, 3, 5, 7) x x x m(1, 5, 9, 13) x x m(2, 3, 6, 7) x x x x m(4, 5, 6, 7) x x x x m(4, 5, 12, 13) x x x m(5 , 7, 13, 15) x x x m(2, 3, 6, 7), m(4, 5, 12, 13), m(5, 7, 13, 15), m(1, 5, 9, 13) are all essential F = a’c + bc’ + bd + c’d 2) F(a,b,c,d) = Σm (3,6,7,15) + Σd(1,2,4,5,11,13,14) Prime Implicant table 3 6 7 15 A m(1, 3, 5, 7) x x B m(2, 3, 6, 7) x x x C m(3, 7, 11, 15) x x D m(4, 5, 6, 7) x x E m(5, 7, 13, 15) x x F m(6, 7, 14, 15) x x = (A + B + C)(B + D)(A + B + D + E + F)(D + E + F)
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