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Chapter 4 計算機算數

Chapter 4 計算機算數. Outline. Problem: Designing MIPS ALU. Functional Specification. A Bit-slice ALU. A 1-bit ALU. A 4-bit ALU. How about Subtraction?. Revised Diagram. Overflow. Overflow Detection. Overflow Detection Logic. Zero Detection Logic. Putting It Altogether (I).

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Chapter 4 計算機算數

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  1. Chapter 4計算機算數

  2. Outline

  3. Problem: Designing MIPS ALU

  4. Functional Specification

  5. A Bit-slice ALU

  6. A 1-bit ALU

  7. A 4-bit ALU

  8. How about Subtraction?

  9. Revised Diagram

  10. Overflow

  11. Overflow Detection

  12. Overflow Detection Logic

  13. Zero Detection Logic

  14. Putting It Altogether (I)

  15. Putting It Altogether (II)

  16. Problems with Ripple Carry Adder

  17. Carry Lookahead: Theory (I)

  18. Carry Lookahead: Theory (II)

  19. Cascaded Carry Lookahead

  20. Carry-select Adder

  21. Add XOR to ALU

  22. Shifters

  23. Combinational Shifter What comes in the MSBs? how many levels for 32-bit shifter? what if we use 4-1 Muxes ?

  24. Outline

  25. Multiplication in MIPS

  26. Division in MIPS

  27. MIPS Multiply/Divide Summary

  28. Unsigned Multiply

  29. Unisigned Multiplier (Ver. 1)

  30. Observations: Multiply Ver. 1

  31. Unisigned Multiplier (Ver. 2)

  32. Unisigned Multiplier (Ver. 3)

  33. Observations: Multiply Ver. 3

  34. Booth’s Algorithm: Motivation

  35. Booth’s Algorithm: Rationale

  36. Booth’s Algorithm

  37. Booths Example (2 x 7)

  38. Booths Example (2 x -3)

  39. Combinational Multiplier

  40. How Does It Work?

  41. Outline

  42. Divide: Paper & Pencil

  43. Divide Hardware (Version 1)

  44. Observations: Divide Version 1

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