01 11 10 0 0 0 0 1 1 1 1 0 1 cover all 1s group

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Unformatted text preview: 1 0 out = 0 0 out 0 c b ab Karnaugh maps identify which inputs are (ir)relevant to the output 00 01 11 10 0 0 0 0 1 1 1 1 0 1 Sum of minterms yields a c 0 0 0 1 1 0 1 0 0 0 1 1 1 1 0 0 1 1 0 1 1 1 1 0 0 1 1 1 0 out = abc + abc + abc + abc 0 0 out 0 c b ab Karnaugh map minimization 00 01 11 10 0 0 0 0 1 1 1 1 0 1 Cover all 1’s Group adjacent blocks of 2n 1’s that yield a rectangular shape Encode the common features of the rectangle out = ab + ac c ab 0 1 c 00 01 11 10 0 1 1 1 0 0 1 Minterms can overlap 0 out = bc + ac + ab ab 00 01 11 10 0 1 1 1 1 1 0 0 1 0 Minterms can span 2, 4, 8 or more cells out = c + ab ab cd 00 01 11 10 00 0 0 0 0 01 1 0 0 1 11 1 0 0 1 10 0 0 0 0 The map wraps around • out = bd ab cd 00 01 11 10 00 1 0 0 1 01 0 0 0 0 11 0 0 0 0 10 1 0 0 1 • out = ab cd 00 01 11 10 00 0 0 0 0 01 1 x x x 11 1 x x 1 10 0 0 0 0 ab cd “Don’t care” values can be interpreted individually in whatever way is convenient • assume all x’s = 1 • out = d 00 01 11 10 00 1 0 0 x 01 0 x x 0 11 0 x x 0 10 1 0 0 1 • assume middle x’s = 0 • assume 4th column x = 1 • out = A multiplexer selects between multiple inputs a • out = a, if d = 0 • out = b, if d = 1...
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