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Reliable Binary Signed Digit Number Adder Design

This paper presents a design for a reliable binary signed digit number adder, focusing on carry-free addition methods. The work examines existing literature on fast adder architectures, including carry-skip, carry-lookahead, and limited carry-free adders. It covers the synthesis results, highlighting performance metrics such as propagation delay, area, and power consumption. Key findings indicate that carry-free addition can facilitate multiple arithmetic operations efficiently, with various coding schemes impacting complexity and timing. This design aims to optimize addition processes in digital systems.

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Reliable Binary Signed Digit Number Adder Design

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  1. Reliable Binary Signed Digit Number Adder Design 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

  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)

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

  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 0 X 1 0 2 0 1 Y 0 1 1 ? 1 p 1 1 -1 e H 1 w -1 1 t 1 0 ? -1 S 1 -1 1 3 4 -2 1

  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 unit is nS Timing Delay Statistic under 0.18 um technology

  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!

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