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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 !!! example
A rod of uniform charge density and length $L$ has a charge density of $p_\ell=\frac{Q}{L}$. 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. 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 ### K-maps
Karnaugh maps are an alternate representation of truth tables arranged by the Gray code. Karnaugh maps are an alternate representation of truth tables arranged by the Gray code.