ECE 275: Digital Design I

Class 10

Adders!!!!

Full Adder

S = A'B'Cin + A'BCin' + AB'Cin' + ABCin S = A'(B ⊕ Cin) + A(B ⊕ Cin)' S = A ⊕ B ⊕ Cin

Cout = A'BCin + AB'Cin + ABCin' + ABCin Cout = Cin(A'B + AB') + AB(Cin' + Cin) Cout = Cin(A ⊕ B) + AB Other forms Cout = AB + Cin(A + B) Cout = AB + BCin + ACin

Form 1

Form 2

Form 3

Would prefer From 3 because it will be be fastest due to Critical Path (the longest path it takes for something to get the result)

Design Problem 1

How do design a full adder using half adders

Design Problem 2

A: A3 A2 A1 A0 B: B3 B2 B1 B0

4-bit Adder

A3 A2 A1 A0 B3 B2 B1 B0 FA <- FA <- FA <- HA S3 S2 S1 S0 Cout

4-bit RCA (Ripple Carry Adder) CLA (Carry Lookahead Adder)

Design Problem 3

Find the 2's Complement of a 4bit number