1 / 19

Unrolling Carry Recurrence

Unrolling Carry Recurrence. Carry-lookahead Equations. 4-bit CLA. Circuit Structure. CLA Complexity. Managing CLA Complexity. Example CLA. Radix-16 Addition. Two Binary Numbers Grouped into Hex Digits Block Generate and Propagate Signals in Each radix-16 Digit

forest
Download Presentation

Unrolling Carry Recurrence

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Unrolling Carry Recurrence

  2. Carry-lookahead Equations

  3. 4-bit CLA

  4. Circuit Structure

  5. CLA Complexity

  6. Managing CLA Complexity

  7. Example CLA

  8. Radix-16 Addition • Two Binary Numbers Grouped into Hex Digits • Block Generate and Propagate Signals in Each radix-16 Digit • Replace c4 Position of CLA Network with Block Signals g[i,i+3] and p[i,i+3] • Results in 4-bit “Lookahead Carry Generator”

  9. CLA Design

  10. Lookahead Carry Generator

  11. Block Generate and Propagate • Assume i0 < i1 < i2 • Example: g[0,3] is Generate Signal of Block for bits 0-3 • Relationships Allow for Merging of Blocks • Can Allow Merged Block to Overlap

  12. Example Merged LAG x15-12 y15-12 x11-8 y11-8 x7-4 y7-4 x3-0 y3-0 CLA 3 CLA 2 CLA 1 CLA 0 c12 c8 c4 c0 g15-12 p15-12 g11-8 p11-8 g7-4 p7-4 g3-0 p3-0 s15-12 s11-8 s7-4 s3-0 Lookahead Carry Generator g15-0 p15-0

  13. CLA Latency

  14. CLA Architecture

  15. Overlapped LAGs • Overlap Blocks [i1,j1] and [i0,j0] • Relationships Become: • Useful for Building Trees of Different Shapes

  16. CLA With LAG

  17. CLA Latency

  18. Ling Adders

  19. Ling Adders – Wired OR

More Related