How does a Computer Add ?

1. How does a Computer Add ? A A AND Gate Output OR Gate Output B B Logic Gates within chips: B Output B Output A A 0 0 0 0 0 0 0 1 1 1 0 0 0 1 0 0 1 1 1 1 1 1 1 1

2. Exclusive OR gate: A XOR Gate Output B B Output A 0 0 0 1 1 0 1 0 1 0 1 1

3. Simple Adder Circuit: 0 XOR Gate Output = 0 + 0 AND Gate 0 Carry over = 0 0 1 XOR Gate Output = 1 + 0 1 AND Gate Carry over = 0 0

4. Simple Adder Circuit: 0 XOR Gate Output = 1 + 1 0 AND Gate Carry over = 0 1 1 XOR Gate Output = 0 + 1 AND Gate 1 Carry over = 1 1

5. Full Adder circuit 0 + 0, carry = 0 Carry over input = 0 0 XOR Gate Output = 0 0 0 AND Gate 0 0 0 XOR Gate + 0 Carry over = 0 0 OR Gate 0 AND Gate 0 0

6. Full Adder circuit 0+1, carry = 0: Carry over input = 0 0 XOR Gate Output = 1 1 0 AND Gate 0 1 1 XOR Gate + 0 Carry over = 0 0 OR Gate 1 AND Gate 0 0

7. Full Adder circuit 1+0, carry = 1: Carry over input = 1 1 XOR Gate Output = 0 1 1 AND Gate 1 1 1 XOR Gate + 0 Carry over = 1 1 OR Gate 1 AND Gate 0 0

8. Multi-Bit Adder: C. C. C. C. X Y Z X . Y . Z . X Y Z X Y Z C.