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Lecture 12b: Adders

Lecture 12b: Adders. Generate / Propagate. Equations often factored into G and P Generate and propagate for groups spanning i:j Base case Sum:. PG Logic. Carry-Ripple Revisited. Carry-Ripple PG Diagram. Carry-Skip Adder. Carry-ripple is slow through all N stages

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Lecture 12b: Adders

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  1. Lecture 12b: Adders

  2. Generate / Propagate • Equations often factored into G and P • Generate and propagate for groups spanning i:j • Base case • Sum: 17: Adders

  3. PG Logic 17: Adders

  4. Carry-Ripple Revisited 17: Adders

  5. Carry-Ripple PG Diagram 17: Adders

  6. Carry-Skip Adder • Carry-ripple is slow through all N stages • Carry-skip allows carry to skip over groups of n bits • Decision based on n-bit propagate signal 17: Adders

  7. Carry-Skip Adder • Carry-ripple is slow through all N stages • Carry-skip allows carry to skip over groups of n bits • Decision based on n-bit propagate signal 17: Adders

  8. Carry-Lookahead Adder • Carry-lookahead adder computes Gi:0 for many bits in parallel. • Uses higher-valency cells with more than two inputs. 17: Adders

  9. Carry-Lookahead Adder • Carry-lookahead adder computes Gi:0 for many bits in parallel. • Uses higher-valency cells with more than two inputs. 17: Adders

  10. Tree Adder • If lookahead is good, lookahead across lookahead! • Recursive lookahead gives O(log N) delay • Many variations on tree adders 17: Adders

  11. PG Diagram Notation 17: Adders

  12. Sklansky 17: Adders

  13. Brent-Kung 17: Adders

  14. Kogge-Stone 17: Adders

  15. Han-Carlson 17: Adders

  16. Knowles [2, 1, 1, 1] 17: Adders

  17. Ladner-Fischer 17: Adders

  18. Taxonomy Revisited 17: Adders

  19. Summary Adder architectures offer area / power / delay tradeoffs. Choose the best one for your application. 17: Adders

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