quartz/content/notes/02-combinatorial-logic.md

title	aliases	tags	sr-due	sr-interval	sr-ease
02-combinatorial-logic		cosc204 lecture	2022-07-19	3	250

• slides

Combinatorial Logic Circuit

[!Definition] Combinatorial Logic Circuit is a circuit whose digital outputs are dependent only on its digital inputs They can be described using logic expressions and therefore logic gates. We assume the outputs respond immediately^[1]

They can be defined:

• Using a truth table

• Using boolean equations (Q\ =\ A+\ B)

• Using graphical symbols

• 1 Bit half adder

• 1 Bit full adder: (includes carry input)

• Ripple carry adder

• 3 Bit parity Generator

  • Adds an extra bit to the input data so that the number of ones in the output is always odd
  • Used for error checking
  • truth table
  • boolean equation
  • circuit

• 7 segment displlay

Boolean Equations

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

De Morgan's Theorum

• (͞A͞+ B) = Ā · B̄

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
• example

Circuit basics:

• current flows + to -
• input to a unit (e.g., LED) is the + end

Logic Gates

• NOT
• AND
• OR
• NAND
• NOR
• XOR/EOR

[^1] : In real circuits propagation delay must be considered, hence the clock cycle on CPUs