1. Binary Addition Section 4.5

2. Binary Addition Example

3. Binary Addition (2)

4. Derivation of ∑ BA∑ 000 101 011 110

5. Derivation of Carry Out Question: What primitive best implements C o ? Inputs: A, B Outputs: C o =A∙B BACoCo 000 100 010 111

6. Implementation of a Half-Adder

7. Limitation of a Half Adder A half-adder does not account for carry-in.

8. Truth Table for a Full Adder carry-in

9. Karnaugh Map For the Sum Bit

10. Karnaugh Map For the Carry-Out Bit

11. Implementation of a Full Adder (carry-in)

12. Four-Bit Adder C 4 is calculated last because it takes C 0 8 gates to reach C 4.

13. Alternative Naming Convention for the Full Adder

14. Hardware Simplification 2 gate delays for C 3 !

15. Four-bit adder with Carry Lookahead