Lecture No. 10
Karnaugh Map and Boolean Expression
Simplification
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Karnaugh Map and Boolean Expression Simplification, Slides of Digital Logic Design and Programming
A detailed explanation of karnaugh maps and their application in simplifying boolean expressions. It covers topics such as standard form of sop and pos expressions, need for standard forms, converting standard sop-pos, minterms & maxterms, and mapping standard and non-standard sop expressions to k-maps. The document also discusses grouping and adjacency in k-maps and simplification of sop expressions using k-maps.
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2011/2012
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Lecture No. 10
Karnaugh Map and Boolean Expression
Simplification
Recap
Examples of Boolean Analysis of Logic
Circuits
Examples of Simplification of Boolean
Expressions
Standard form of SOP and POS
expressions
Karnaugh Map
Simplification of Boolean Expressions
Doesn’t guarantee simplest form of
expression
Terms are not obvious
Skills of applying rules and laws
K-map provides a systematic method
An array of cells
Used for simplifying 2, 3, 4 and 5 variable
expressions
3-Variable K-map
AB\C 0 1
A\BC 00 01 11 10
Grouping & Adjacent Cells
K-map is considered to be wrapped
around
All sides are adjacent to each other
Groups of 2, 4, 8,16 and 32 adjacent cells
are formed
Groups can be row, column, square or
rectangular.
Groups of diagonal cells are not allowed
Mapping of Standard SOP expression
Selecting n-variable K-map
1 marked in cell for each minterm
Remaining cells marked with 0
Mapping of Standard SOP expression
SOP expression
A .B .C.D+A.B.C.D+ A.B.C.D+A.B.C.D+A.B.C.D+A.B.C.D+A.B.C. D
AB\CD 00 01 11 10
Mapping of Non-Standard SOP expression
Selecting n-variable K-map
1 marked in all the cells where the non-
standard product term is present
Remaining cells marked with 0
Mapping of Non-Standard SOP expression
SOP expression
AB\C 0 1
A\BC 00 01 11 10
A +B C
Mapping of Non-Standard SOP expression SOP expression (^) D + AC +BC AB\CD 00 01 11 10 00 0 1 1 0 01 0 1 1 0 11 0 1 1 0 10 0 1 1 0
Mapping of Non-Standard SOP expression SOP expression (^) D + AC +BC AB\CD 00 01 11 10 00 0 1 1 0 01 0 1 1 1 11 1 1 1 1 10 1 1 1 0
Simplification of SOP expressions using K-map
Mapping of expression
Forming of Groups of 1s
Each group represents product term
3-variable K-map
1 cell group yields a 3 variable product term
2 cell group yields a 2 variable product term
4 cell group yields a 1 variable product term
8 cell group yields a value of 1 for function
Simplification of SOP
expressions using K-map
AB\C
A\BC
B. C + A.C +B. C A .B .C + A.C + A. B
Simplification of SOP
expressions using K-map
AB\C
A\BC
B + A. C A .B +B.C + A. B