1. Basic Addition Review Basic Adders and the Carry Problem Carry Propagation Speedup Speed/Cost Tradeoffs Two-operand Versus Multi-operand Adders

2. Half Adders

3. Adder Equations

4. Full Adder F (A,B,C) = A  B  C G = AB + AC + BC AB S CiCo Cin AB Cout Sum Sum = A  B  Cin Cout = AB + Cin A + Cin B = AB + Cin (A + B) Full Adder (FA)

5. 4-Bit Ripple Carry Adder AB S CiCo AB S CiCo AB S CiCo AB S CiCo Cin A(0) Cout B(0)A(1)B(1)A(2)B(2)A(3)B(3) C(0)C(1)C(2)C(3)C(4) Sum(0)Sum(1)Sum(2)Sum(3) A[3:0] B[3:0] SUM[3:0] + C[0] C[4]

6. Full Adder Implementations

7. Adder Circuits Using FA

8. Ripple Carry Adder Layout

9. Delay in Ripple Adder

10. Adders as Logic Elements

11. Adder Exceptions

12. Adder Exception Circuitry

13. Carry Propagation Analysis

15. Carry Completion Detection

16. Counters

17. Asynchronous up-Counter

18. Three-stage up-Counter

19. Generate, Propagate and Kill

20. Transfer Signal

21. Manchester Carry Chain