Karnaugh Maps.md (870B)
1 +++ 2 title = 'Karnaugh maps' 3 +++ 4 # Karnaugh maps 5 ## Given a truth table: 6 7 | | x₁ | x₂ | x₃ | ƒ₁ | 8 | --- | --- | --- | --- | --- | 9 | m₁ | 0 | 0 | 0 | 1 | 10 | m₂ | 0 | 0 | 1 | 1 | 11 | m₃ | 0 | 1 | 0 | 0 | 12 | m₄ | 0 | 1 | 1 | 1 | 13 | m₅ | 1 | 0 | 0 | 0 | 14 | m₆ | 1 | 0 | 1 | 0 | 15 | m₇ | 1 | 1 | 0 | 0 | 16 | m₈ | 1 | 1 | 1 | 1 | 17 18 ## Make a table such as this: 19 Adjacent cells can only differ in one bit! 20 21 | A/BC | 00 | 01 | 11 | 10 | 22 | --- | --- | --- | --- | --- | 23 | 0 | m₁: 1 | m₂: 1 | m₄: 1 | m₃: 0 | 24 | 1 | m₅: 0 | m₆: 0 | m₇: 0 | m₈: 1 | 25 26 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.