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.