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

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