Chapter3_2 - Chapter 3 (Lect 2) Gate-Level Minimization...

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Chapter 3 (Lect 2) Gate-Level Minimization K-Maps (sum-of-products) Two – Variable Three – Variable Four – Variable Five – Variable K-Maps (product-of-sums) Don’t Care Conditions
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Karnaugh or K-maps: Is a diagram of squares containing minterms of a function to be minimized Provides a graphical method for minimizing Boolean expressions Recall a minimized expression produces a simpler circuit Procedure: 1. Draw and label the 2, 3, or 4 variable K-map. 2. Literal values must be ordered such that only one literal changes value between adjacent blocks. 3. Group adjacent 1’s in sets of 2, 4, or 8 (power of 2) 4. Form the sum-of-products using the variables of each grouped set whose values do not change. 5. All squares containing 1’s must be used at least once and can be used more than once
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x’y’ y 0 1 0 1 m 00 =m 0 m 01 =m 1 m 10 =m 2 m 11 =m 3 x’y xy’ xy x
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(, ) ( 2 ,3 ) Fxy =
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x yz 0 1 00 01 11 10 m 0 m 1 m 3 m 2 m 4 m 5 m 7 m 6 ( , , ) (2,3,5) Fxyz =
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( , , ) (2,3,4,5) Fxyz = '' ' ' ' Fx zy zx y z = ++
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AB CD m 0 00 01 11 10 00 01 10 m 1 m 3 m 2 m 4 m 5 m 7 m 6 m 12 m 8 m 13 m 15 m 14 m 9 m m 10
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( , , , ) (1, 2,5,6,8,9,12,13,14) FABCD =
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''' ' ' ' ' '' F ABC BCD ABCD ABC = ++ + 4–corners!
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BC BC DE DE 00 01 11 10 00 01 10 00 01 10 00 01 10 A = 0 A = 1 1 1 1 1 1 1 1 1 1 1 1
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Chapter3_2 - Chapter 3 (Lect 2) Gate-Level Minimization...

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