LOGIC5_r2 - Chapter 5 Karnaugh Maps Microwave &...

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Chapter 5 Karnaugh Maps
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Just like a truth table, the Karnaugh map of a function specifies the value of the function for every combination of the independent variables. Construction of Kanaugh Maps : 2-Variable B A 0 1 a 0 a 2 a 1 a 3
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3-Variable BC A 0 1 a 0 a 4 a 1 a 5 a 3 a 7 a 2 a 6
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4-Variable AB CD 00 01 11 10 a 0 a 4 a 12 a 8 a 1 a 5 a 13 a 9 a 3 a 7 a 15 a 11 a 2 a 6 a 14 a 10
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5-Variable A 1/0 DE BC 00 01 11 10 16 0 20 4 28 12 24 8 17 1 21 5 29 13 25 9 19 3 23 7 31 15 27 11 18 2 22 6 30 14 26 10
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Remark : (1) Each 1 on the map corresponds to a minterm of F . (2) Minterms in adjacent squares of the map can be combined since they differ in only one variable .
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EX : A B F 0 0 1 0 1 1 1 0 0 1 1 0 B A 0 1 1 0 1 0 Since F= Σ m(0,1)=m 0 +m 1 =A’B’+A’B=A’(B’+B)=A’
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EX : A B F 0 0 1 0 1 0 1 0 1 1 1 1 B A 0 1 F=B’+A 1 1 0 1 Since F = m0+m2+m3 = A’B’+AB’+AB = A’B’+AB’+AB+AB’=B’+A
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EX : A B C F 0 0 0 0 0 0 1 0 0 1 0 1 0 1 1 1 1 0 0 0 1 0 1 1 1 1 0 1 1 1 1 1
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BC A 0 1 F=B+AC 0 0 0 1 1 1 1 1 F=m 2 +m 3 +m 5 +m 6 +m 7 =A’BC’+A’BC+AB’C+ABC’+ABC+ABC =A’B+AC+AB=B+AC
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EX :
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This note was uploaded on 10/23/2011 for the course EE 101 taught by Professor Wang during the Spring '11 term at Illinois State.

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LOGIC5_r2 - Chapter 5 Karnaugh Maps Microwave &...

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