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@@ -0,0 +1,58 @@ +[\<- Karnaugh Maps, Prime Implicants](4.md) + +--- + +# Additional K-map concepts: solving for 0's and use of don't cares + +## Using the 0's in a K-map + +### Consider the 0's + +- Sometimes targeting the 0's yields a lower cost solution + - Cost = #gates + #inputs to all gates +- Apply the same process of identifying PI's, but use the 0's instead of the 1's + - Same as if we created K-map for the inverse of the functnio; call if g (=!f) + +### POS example + +- !f = `!x3*!x4 + !x2*!x3 + x1*x2*x3*x4` +- f = `!(!x3*!x4 + !x2*!x3 + x1*x2*x3*x4)` +- f = `(x3+x4) * (x2+x3) * (!x1+!x2+!x3+!x4)` + + + +--- + +## The concept and use of don't cares + +### Don't Cares + +- Sometimes you know certain input combinations can't happen + - You "don't care" how the logic handles it (wildcard) +- Include in an implicant to give it more coverage => "smaller" product terms + + + +--- + +## Example of 7-segment display + +- If you draw an "8" with equal-sized straight lines, there will be 7 such line "segments" +- All decimal digits (0-9) can be represented using a subset of these 7 segments +- A 7-segment display has 7 inputs, one for each segment + - An assertion (1) causes that segment to light +- How to convert a 4-bit value, representing a number from 0-9, into the correct 7 controls? + + + +--- + +## Summary of how to make use of don't cares + +### K-maps with don't cares + +- Our general process is to try to find the largest PIs possible +- Use don't cares to create larger PIs + - Creates a product term with fewer variables + - Applies whether solving for 1's or 0's +- A don't care cell does \*not\* make a PI essential |