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35 lines
1.1 KiB
Markdown
35 lines
1.1 KiB
Markdown
---
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title: "boolean-equations"
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aliases:
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tags:
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- cosc204
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---
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Often used to describe/define [combinatorial-logic-circuit](notes/combinatorial-logic-circuit.md)
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# Precedence
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Precedence
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- NOT is unary, so it has the highest precedence
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- AND is mulitply, so it comes next
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- OR is like plusl, to it comes last
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# Creating boolean equations
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Creating boolean equations:
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- for each row where output is 1
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- write the equation as a function of the inputs (using AND)
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- Write the final equation, putting OR between each clause
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# De Morgan's Theorum
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- !(A + B) = A! & !B
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- !(A + B + C + ... + X) = !A & !B & !C & ... & !X
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- [truth table](https://i.imgur.com/QegVxkx.png)
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- any boolean function can be represented as the sum of logical products
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- All combinatorial circuits can be described using just one gate type (either nand or nor) [^2]
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[^2] : The Apollo Guidance Computer used about 5600 NOR gates and no other gate types! |