Karnaugh Map and Boolean Expression Simplification, Slides of Digital Logic Design and Programming

Download Karnaugh Map and Boolean Expression Simplification and more Slides Digital Logic Design and Programming in PDF only on Docsity!

Lecture No. 11

Karnaugh Map and Boolean Expression

Simplification

Recap

 Karnaugh Maps

 Mapping Standard SOP expressions

 Mapping Non-Standard SOP expressions

 Simplification of K-maps

 Don’t care states

Mapping of Standard POS expression

 POS expression

AB\C 0 1

A\BC 00 01 11 10

( A +B + C).(A +B + C).(A +B + C).(A +B + C )

Simplification of POS expressions using K-map

 Mapping of expression

 Forming of Groups of 0s

 Each group represents sum term

 3-variable K-map

 1 cell group yields a 3 variable sum term

 2 cell group yields a 2 variable sum term

 4 cell group yields a 1 variable sum term

 8 cell group yields a value of 0 for function

Simplification of POS

expressions using K-map

AB\C

A\BC

(B + C).(A +B + C ) ( A +B +C).(A +C).(A +B )

Simplification of POS

expressions using K-map

AB\C

A\BC

( A +B).(B +C ) ( A +B).(A +B + C )

Simplification of POS

expressions using K-map

AB\CD 00 01 11 10

( A +C).(C +D).(B +C +D )

Simplification of POS

expressions using K-map

AB\CD 00 01 11 10

( A +B +C).(A +B +D).(B +C+D).(A +B +C+D )

Conversion between SOP &

POS using K-map

AB\CD 00 01 11 10

BD +BC+ ABC+ ABD + AC D

5-Variable K-map

 Represented as two, 4 variable K-map

5-Varaible K-map

BC\DE 00 01 11 10

A = 1

Simplification of a 5-Variable K-map

 5 variable K-map mapping

 5 variable K-map grouping

 5 variable K-map simplification

5-Varaible K-map simplification BC\DE 00 01 11 10 00 1 1 0 0 01 1 1 0 0 11 0 0 0 1 10 0 1 1 1

A = 1

Functions having multiple outputs

 Ckt receives a BCD number input

 Displays decimal number 0 to 9 on a

single digit 7-segment display

 Ckt receives two 2-bit numbers A and B

 Sets one of three outputs to >, =, or <