Number Systems and Circuits for Addition

Lecture 5

Section 1.5

Thu, Jan 26, 2006

Binary Addition

Addition of binary digits produces a sum bit and a carry bit.

p q sum carry

0 0 0 0

0 1 1 0

1 0 1 0

1 1 0 1

Binary Addition

The sum bit is p q. The carry bit is p q.

Binary Adders

A binary half-adder adds two bits and produces a sum bit and a carry bit.

A binary full-adder adds two bits and a carry-in bit and produces a sum bit and a carry-out bit.

Binary Half-Adder Circuit

Design circuits for p q and p q. Consolidate them into one circuit, if

possible.

Binary Full-Adder Circuit

Input Output

p q c-in s c-out

0 0 0 0 0

0 1 0 1 0

1 0 0 1 0

1 1 0 0 1

0 0 1 1 0

0 1 1 0 1

1 0 1 0 1

1 1 1 1 1

Binary Full-Adder Circuit

Use two half-adders to add the bits two at a time.Add p and q, producing s1 and c1.

Add c-in and s1, producing s and c2.

Add c1 and c2, producing c-out.

• c1 c2 produces c-out.

Design the circuit.