Logic Gates

NOT Gate

Also known as an inverter

x ~x

AND Gate

x

y

xy

OR Gate

x

y

x+y

XOR Gate

x

y

x XOR y

What are digital circuits?

System of logic components that model some Boolean expression

Inputs Digital Circuit Output Example: ~x · y = z

x

yz

Example – Circuit Expression

What Boolean function does the following digital circuit model?

Answer: ~x + ~y = z

x

y

z

Example – Circuit Expression

What Boolean function does the following digital circuit model?

Answer: f = xy + yz + ~xz

x

y

zf

Your Turn

What Boolean function does the following digital circuit model?

x

y

z

f

Example – Expression Circuit

Draw the logic circuit that corresponds to the following Boolean expression: f = ~(xy+z)

x

y

zf

Example – Expression Circuit

Draw the logic circuit that corresponds to the following Boolean expression: f = ~(x+z)·(x+y)

x

y

z

f

Your Turn

Draw the logic circuit that corresponds to the following Boolean expression:

f = xy + ~xy + ~(yz)

NAND Gate

~(xy)

x

y~(xy)

x

y~(xy)

NOR GATE

~(x+y)

x

y~(x+y)

x

y

~(x+y)