1. Number Systems and Circuits for Addition
Lecture 5
Section 1.5
Wed, Jan 19, 2005

2. Binary Addition
Addition of binary digits produces a sum bit and a carry bit. p q
sum
carry 1

3. Binary Addition
The sum bit is p  q.
The carry bit is p  q.

4. 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.

5. Binary Half-Adder Circuit
Design circuits for p  q and p  q.
Consolidate them into one circuit, if possible.

6. Binary Full-Adder Circuit
Input
Output p q
c-in s
c-out 1

7. 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.