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ece124: add k-maps

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eggy 2023-01-24 19:00:37 -05:00
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@ -266,6 +266,18 @@ The 1-bit Gray code is $0, 1$. To convert an $n$-bit Gray code to an $n+1$-bit G
Sorting truth table inputs in the order of the Gray code makes optimisation easier to do.
### K-maps
Karnaugh maps are an alternate representation of truth tables arranged by the Gray code.
- Coordinates are the input values to the function
- The output square of the coordinates is the output value of the function
- Headers are sorted by Gray code (multiple variables can be combined by increasing the number of bits in the Gray code)
Each square is effectively a minterm, and finding the least number of rectangles that only cover "1"s allows for the simplest algebraic form of the truth table to be deduced. If needed, rectangles can wrap around on any side.
<img src="https://upload.wikimedia.org/wikipedia/commons/b/b7/K-map_6%2C8%2C9%2C10%2C11%2C12%2C13%2C14.svg" width=500>(Source: Wikimedia Commons)</img>
## VHDL
VHDL is a hardware schematic language.