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 	- An essential PI contains cells that are not part of any other PI
 - Write the SOP equation, starting with the essential PI's
 	- Add the minimum number of non-essential PI's needed to "cover" all cases where the function should evaluate to true
+
+---
+
+[Additional K-map concepts: solving for 0's and use of don't cares ->](5.md)
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+[\<- 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)`
+
+![diagram](5.1.png)
+
+---
+
+## 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
+
+![diagram](5.2.png)
+
+---
+
+## 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?
+
+![diagram](5.3.png)
+
+---
+
+## 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