Gates and Circuits

Three Main Gates  AND  OR  NOT

NAND Gates  NOT AND TFF TTF TFT FTT A NAND BBA

Gate Diagrams  Example: MR + S

Gate Diagrams  Example:

Gate Diagrams  Example: (MR + S) (RS)’

Gate Diagrams  Exercise:

Truth Table (to Expression) to Gates  First, build the Boolean algebra expression that gives Z Z = AB + A’B’ TFF FTF FFT TTT ZBA

Truth Table to Gates  Z = AB + A’B’  Next, build the circuit that goes with the Boolean algebra expression Z TFF FTF FFT TTT ZBA

Z = AB + A’B’

Boolean Expression to Gates  Exercise: (A + B’) A

Boolean Expression to Gates  Exercise: (A + B’) A

Multi-input AND and OR  What circuit corresponds to ABC?  A+B+C?

Binary Addition  The first step in building our computer…

Binary Addition TrueFalse True False Sum Carry

Binary Addition CarryBA SumBA

Sum Circuit SumBA Sum = AB’ + A’B

Carry Circuit CarryBA Carry = AB

Half Adder - Sum and Carry

Full Adder

4 Bit Adder  Computers represent numbers in parallel.

Exercises  Give Boolean expressions and construct circuits with the following properties (using AND, OR or NOT gates):

Exercises A)B)‏ ZBA ZCBA

Exercises  2 - Fill in a truth table and give a Boolean expression for the following circuit.