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ece124: add don't care

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eggy 2023-01-26 15:03:20 -05:00
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docs/1b/ece106.md
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@ -214,3 +214,10 @@ $$dQ=\rho_s dS$$
!!! example
A rod of uniform charge density and length $L$ has a charge density of $p_\ell=\frac{Q}{L}$.
1. Determine the formula for the charge density $\rho$
2. Choose an origin and coordinate system (along the axes of the object when possible)
3. Choose an arbitrary point $A$ on the charge
4. Create a right-angle triangle with $A$, the desired point, and usually the origin
5. Attempt to find symmetry
6. Solve

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docs/1b/ece124.md
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@ -266,6 +266,10 @@ 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.
A **"don't care"** is represented by a $d$ in truth tables. It is used for optimisation if the state of that output doesn't matter, and can be treated as a one or a zero as desired.
It can be more efficient to optimise two different functions differently such that they are more optimised when combined.
### K-maps
Karnaugh maps are an alternate representation of truth tables arranged by the Gray code.