Systems Architecture

Table of Contents

Karnaugh maps

Given a truth table:

x₁x₂x₃ƒ₁
m₁0001
m₂0011
m₃0100
m₄0111
m₅1000
m₆1010
m₇1100
m₈1111

Make a table such as this:

Adjacent cells can only differ in one bit!

A/BC00011110
0m₁: 1m₂: 1m₄: 1m₃: 0
1m₅: 0m₆: 0m₇: 0m₈: 1

Then choose groups of 1s of size 2ⁿ. They should be as big as possible. Then you see what changes within the groups, and if a bit changes to its complement so that it cancels out to 1, you don’t have to include it.