1. Han Liu Supervisor: Seok-Bum Ko Electrical & Computer Engineering Department 2010-Feb-23

2. Outline Information of literature Background Carry Free Adder Limited Carry Free Adder Synthesis Result Conclusion 2

3. Information of literature Reliable Binary Signed Digit Number Adder Design F. Kharbash, G. M. Chaudhry IEEE Computer Society Annual Symposium on VLSI(ISVLSI'07) 3

4. Background Fast Adder Architecture Carry Skip Adder Carry Look-ahead Adder Carry Save Adder Carry Free Adder Limited Carry Free Adder 4

5. Carry Free Addition 1/4 Redundancy Representation of numbers is not unique Redundancy may result from narrowing the range of represented values (e.g. 1's compl.) Redundancy may result from adopting the digit set wider than radix ({-1,0,1} in radix 2) Conversion is a carry-propagate (slow) process

6. Carry Free Addition 2/4 Reduction of digit set by carry propagation by only one position P=10*T+W P is preliminary results T is transfer digits W is immediate sums

7. Carry Free Addition 3/4 Two-Stage Carry Free Adder

8. Carry Free Addition 4/4 Coding Schemes influence on complexity sign+value BSD: -1 (11), 0 (00), 1 (01) 2's complement BSD: -1 (11), 0 (00), 1 (01) negative-positive flags ([-1,1] only) BSD: -1 (10), 0 (00), 1 (01) 1-out-of-n BSD: -1 (100), 0 (010), 1 (001)

9. Limited Carry Free Addition 1/3 When redundancy is not enough, the free carry propagation cannot be guaranteed 1 1 1 1 0 0 0 0 1 1 1 1 ? ? 1 1 1 1 0 0 0 0 1 1 0 0 1 1 H H 1 1 1 1 ? ? 1 1 1 1 2 1 3 4-21 X Y p e w t S

10. Limited Carry Free Addition 2/3 Three -Stage Limited Carry Free Adder

11. Limited Carry Free Addition 3/3 1-out-of-3 SD number

12. Synthesis Result 1/2 Timing Delay Statistic under 0.18 um technology unit is nS

13. Synthesis Result 2/2 Area and Power Consumption Statistic

14. Conclusion Propagation delay in Carry Free Adder is independent with input bit width Different coding schemes have different complexity and timing delay Conversion after the CFA still generate delay CFA is suitable in multiple addition stages process CFA is suitable if redundancy is enough (ie. BCD number in decimal addition)

15. Question Thanks! 15