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Sorter

Sorter. Discuss in full detail the flow-diagram of a sorter Derive the pipelined circuit from this diagram Derive combinational butterfly circuit from this diagram Derive Ping-Pong architecture with a controller and data Path from this diagram.

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Sorter

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  1. Sorter • Discuss in full detail the flow-diagram of a sorter • Derive the pipelined circuit from this diagram • Derive combinational butterfly circuit from this diagram • Derive Ping-Pong architecture with a controller and data Path from this diagram. • Discuss other applications of the flow-diagram idea.

  2. Data Flow for a sorter

  3. We can derive butterfly pipeline from this diagram • We can derive combinational butterfly from this diagram. • There are many circuits that use MIN/MAX 2*2 sorter as a component of larger architectures.

  4. Programming • SA --- Systolic Array • SIMD ---Single Instruction Multiple Data • ISA ---Instruction Systolic Array • MIMD ---Multiple Instruction Multiple Data We will compare on examples the systolic merge architecture and the ISA merge architecture

  5. parallel merge initial situation: 1.) sort columns (odd-even-transposition sort) 2.) sort rows (odd-even-transposition sort) sorted !!!! x1 x2 x3 x4 x5 x6 ... x7 ... x17 x18 y1 y2 y3 y4 y5 y6 ... y7 ... y17 y18

  6. 0s 1s initially 0s 0s after vertical sort 1s 0s after horizontal sort 1s 0-1 principle • The 0-1 principle states that if all sequences of 0 and 1 are sorted properly than this is a correct sorter. • The sorter must be based on moving data.

  7. MIMD-mesh (clocked) min max Time: 2n

  8. 1 3 3 4 5 5 6 7 9 8 8 7 4 4 3 2 systolic merge

  9. 1 3 3 4 5 5 6 7 9 8 8 7 4 4 3 2 systolic merge

  10. 1 3 3 4 5 5 6 7 9 8 8 7 4 4 3 2 systolic merge

  11. 1 3 3 4 5 5 6 7 9 8 8 7 4 4 3 2 systolic merge

  12. 1 3 3 4 5 5 6 7 9 8 8 7 4 4 3 2 1 3 3 4 5 5 6 7 4 4 3 2 9 8 8 7 systolic merge

  13. 1 3 3 4 5 5 6 7 4 4 3 2 9 8 8 7 systolic merge

  14. 1 3 3 4 4 4 3 2 5 5 6 7 9 8 8 7 systolic merge

  15. 1 3 3 4 4 4 3 2 5 5 6 7 9 8 8 7 systolic merge

  16. 1 3 3 2 4 4 3 4 5 5 6 7 9 8 8 7 systolic merge

  17. 1 3 3 2 4 4 3 4 5 5 6 7 9 8 8 7 systolic merge

  18. 1 3 3 2 4 4 3 4 5 5 6 7 9 8 8 7 systolic merge

  19. 1 3 2 3 4 3 4 4 5 5 6 7 9 8 8 7 systolic merge

  20. 1 3 2 3 4 3 4 4 5 5 6 7 9 8 8 7 systolic merge

  21. 1 2 3 3 3 4 4 4 5 5 6 7 9 8 8 7 systolic merge

  22. 1 2 3 3 3 4 4 4 5 5 6 7 9 8 8 7 systolic merge

  23. 1 2 3 3 3 4 4 4 5 5 6 7 9 8 8 7 systolic merge

  24. 1 2 3 3 3 4 4 4 5 5 6 7 8 9 7 8 systolic merge

  25. 1 2 3 3 3 4 4 4 5 5 6 7 8 9 7 8 systolic merge

  26. 1 2 3 3 3 4 4 4 5 5 6 7 8 7 9 8 systolic merge

  27. 1 2 3 3 3 4 4 4 5 5 6 7 8 7 9 8 systolic merge

  28. 1 2 3 3 3 4 4 4 5 5 6 7 7 8 8 9 systolic merge • sorted !!!

  29. C:=min{C, CE} C:=max{C, CW} 1 3 3 4 5 5 6 7 9 8 8 7 4 4 3 2 ISA merge Array to be sorted

  30. 1 3 3 4 5 5 6 7 9 8 8 7 4 4 3 2 ISA merge

  31. 1 3 3 4 5 5 6 7 9 8 8 7 4 4 3 2 ISA merge

  32. 1 3 3 4 5 5 6 7 9 8 8 7 4 4 3 2 ISA merge

  33. 1 3 3 4 5 5 6 7 9 8 8 7 4 4 3 2 ISA merge

  34. 1 3 3 4 5 5 6 7 4 8 8 7 9 4 3 2 ISA merge

  35. 1 3 3 4 5 5 6 7 4 8 8 7 9 4 3 2 ISA merge

  36. 1 3 3 4 4 5 6 7 5 4 8 7 9 8 3 2 ISA merge

  37. 1 3 3 4 4 5 6 7 5 4 8 7 9 8 3 2 ISA merge

  38. 1 3 3 4 4 4 6 7 5 5 3 7 9 8 8 2 ISA merge

  39. 1 3 3 4 4 4 6 7 5 5 3 7 9 8 8 2 ISA merge

  40. 1 3 3 4 4 4 3 7 5 5 6 2 9 8 8 7 ISA merge

  41. 1 3 3 4 4 4 3 7 5 5 6 2 9 8 8 7 ISA merge

  42. 1 3 3 4 4 4 3 2 5 5 6 7 9 8 8 7 ISA merge

  43. 1 3 3 4 4 4 3 2 5 5 6 7 9 8 8 7 ISA merge

  44. 1 3 3 2 4 4 3 4 5 5 6 7 9 8 8 7 ISA merge

  45. 1 3 3 2 4 4 3 4 5 5 6 7 9 8 8 7 ISA merge

  46. 1 3 2 3 4 3 4 4 5 5 6 7 9 8 8 7 ISA merge

  47. 1 3 2 3 4 3 4 4 5 5 6 7 9 8 8 7 ISA merge

  48. 1 2 3 3 3 4 4 4 5 5 6 7 9 8 8 7 ISA merge

  49. 1 2 3 3 3 4 4 4 5 5 6 7 9 8 8 7 ISA merge

  50. 1 2 3 3 3 4 4 4 5 5 6 7 9 8 8 7 ISA merge

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