quartz/content/notes/boolean-equations.md

title	aliases	tags
boolean-equations		cosc204

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!