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| title | aliases | tags | |
|---|---|---|---|
| boolean-equations |
|
Often used to describe/define Combinatorial logic circuits
Precedence
Precedence
- NOT is unary, so it has the highest precedence
- AND is mulitply, so it comes next
- OR is like plusl, to it comes last
Creating boolean equations
Creating boolean equations:
- for each row where output is 1
- write the equation as a function of the inputs (using AND)
- Write the final equation, putting OR between each clause
De Morgan's Theorum
- !(A + B) = A! & !B
- !(A + B + C + ... + X) = !A & !B & !C & ... & !X
- truth table
- any boolean function can be represented as the sum of logical products
- All combinatorial circuits can be described using just one gate type (either nand or nor) [^2]
[^2] : The Apollo Guidance Computer used about 5600 NOR gates and no other gate types!