lecture06

# lecture06 - corresponding to A = 0 b 1 corresponding to A =...

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CMPT 150 K-maps Page 1 K-map example b We had f(x,y,z) = m(1,3,6), let’s draw the k-map: b Notice that each minterm in the k-map has 3 neighbours, which is the same as the number of variables. CMPT 150 K-maps Page 2 4-Variable K-map b A four variable k-map looks like this: A B C D F 0 0 0 0 0 0 0 1 0 0 1 0 0 0 1 1 m 0 m 1 m 2 m 0 1 0 0 0 1 0 1 0 1 1 0 0 1 1 1 1 0 0 0 1 0 0 1 1 0 1 0 1 0 1 1 1 1 0 0 1 1 0 1 1 1 1 0 1 1 1 1 3 m 4 m 5 m 6 m 7 m 8 m 9 m 10 m 11 m 12 m 13 m 14 m 15 CMPT 150 K-maps Page 3 4-Variable K-map Example E.g. f(A,B,C,D) = m( A B C D F 0 0 0 0 0 0 0 1 0 0 1 0 0 0 1 1 1 0 1 0 0 1 0 0 0 1 0 1 0 1 1 0 0 1 1 1 1 0 0 0 1 0 0 1 1 0 1 0 1 0 1 1 1 1 0 0 1 1 0 1 1 1 1 0 1 1 1 1 0 0 1 0 1 0 1 0 0 0 1 1 CMPT 150 K-maps Page 4 Product of Sums b What if we circle groups of zeroes instead of ones? b b This is F represented as product of sums b Can use either method, depending on your preference

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CMPT 150 K-maps Page 5 Larger k-maps b How can we have 5 variable k-maps? b Each minterm has ____ neighbours b We have to start “stacking” the 4-variable maps b E.g. for F(A,B,C,D,E), we have 2 4-variable maps
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Unformatted text preview: corresponding to A = 0 b 1 corresponding to A = 0 b 1 corresponding to A = 1 b Obviously things become more complicated! b What about 6 variable k-maps? b How many 4-variable maps would we need? Answer: CMPT 150 K-maps Page 6 The “don’t care” Condition b Some truth tables are incompletely specified b Sometimes there are some inputs where function can be anything, these are called the “don’t care” inputs b We describe them using f and d : b f = ∑ m(i,j,k, … ) to list minterms where f = 1 b d = ∑ m(l,m,n, … ) to list minterms where f is “don’t care” b How can we use these inputs? b List “don’t care” inputs in k-map with an x b Treat the x ’s as either 1 or 0 to create bigger rectangles CMPT 150 K-maps Page 7 “Don’t care” conditions example E.g. f(a,b,c) = ∑ m(1,6) d(a,b,c) = ∑ m(3,4,5,7)...
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lecture06 - corresponding to A = 0 b 1 corresponding to A =...

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