# lec4 - CS 140 Lecture 4 Combinational Logic K-Map Professor...

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CS 140 Lecture 4 Combinational Logic: K-Map Professor CK Cheng CSE Dept. UC San Diego 1

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Part I. Combinational Logic Implementation K-map 2
4-Variable K-Maps: An example f(a,b,c,d) Id a b c d f (a,b,c,d) 0 0 0 0 0 0 1 0 0 0 1 0 2 0 0 1 0 1 3 0 0 1 1 1 4 0 1 0 0 0 5 0 1 0 1 0 6 0 1 1 0 1 7 0 1 1 1 1 8 1 0 0 0 0 9 1 0 0 1 0 10 1 0 1 0 1 11 1 0 1 1 1 12 1 1 0 0 0 13 1 1 0 1 0 14 1 1 1 0 1 15 1 1 1 1 1 3

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Corresponding K-map f (a, b, c, d) = c b c a d 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 4 12 8 1 5 13 9 3 7 15 11 2 6 14 10 4
Another example w/ 4 bits: Id a b c d f (a,b,c,d) 0 0 0 0 0 1 1 0 0 0 1 1 2 0 0 1 0 1 3 0 0 1 1 0 4 0 1 0 0 0 5 0 1 0 1 0 6 0 1 1 0 0 7 0 1 1 1 0 8 1 0 0 0 1 9 1 0 0 1 - 10 1 0 1 0 - 11 1 0 1 1 0 12 1 1 0 0 0 13 1 1 0 1 0 14 1 1 1 0 1 15 1 1 1 1 0 5

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Corresponding 4-variable K-map f (a, b, c, d) = b’c’ + b’d’ + acd’ b c a d 1 0 0 1 1 0 0 - 0 0 0 0 1 0 1 - 0 4 12 8 1 5 13 9 3 7 15 11 2 6 14 10 6
Boolean Expression K-Map Variable x i and its compliment x i Two half planes Rx i , and Rx i Product term P

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lec4 - CS 140 Lecture 4 Combinational Logic K-Map Professor...

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