Karnaugh Maps-Digital Electronics Tutorials

Technique to simplify logic

Map output onto grid based on input Left, right, up, down, change by only one input One K-Map per output equation desired Produce Sum of Products (SOP) by circling ones

To produce a SOP:

Circle each 1 at least once
For each circle that circles multiple 1’s, a term is dropped
Must be circled in powers of 2 (1, 2, 4, 8)
Cannot circle diagonally

Example
3 input (A,B,C) yields a single output (X)

K-Map

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Circle all 1’s at least once

A=0 Row
C changes between 0 and 1
Drop C and take the other two inputs
1st term = !A B

B=1, C=1 column
A changes between 0 and 1
Drop A and take the other two inputs
2nd term = BC

A=1,B=0, C=0 term
Only one to circle, no simplification
Take term literally

3rd term = A!B!C

Result
X = !AB + BC + A!B!C
Required logic
2 2 input AND gates
1 3 input AND gate
1 3 input OR gate

Video Tutorials:



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