1. Number Systems and Circuits for Addition – Binary Adders Lecture 6 Section 1.5 Fri, Jan 26, 2007

2. Binary Addition Addition of binary digits produces a sum bit and a carry bit. pqsumcarry 0000 0110 1010 1101

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 InputOutput pqc-insc-out 00000 01010 10010 11001 00110 01101 10101 11111

7. Binary Full-Adder Circuit Use two half-adders to add the bits two at a time. Add p and q, producing s 1 and c 1. Add c-in and s 1, producing s and c 2. Add c 1 and c 2, producing c-out. c 1  c 2 produces c-out. Design the circuit.

8. Adding 4-Bit Numbers Design a circuit using four full adders to add two 4-bit binary numbers.