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Arithmetic Building Blocks

Arithmetic Building Blocks

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Arithmetic Building Blocks

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  1. Arithmetic Building Blocks

  2. A Generic Digital Processor

  3. Building Blocks for Digital Architectures Arithmetic unit Bit-sliced datapath adder - ( , multiplier, shifter, comparator, etc.) Memory - RAM, ROM, Buffers, Shift registers Control - Finite state machine (PLA, random logic.) - Counters Interconnect - Switches - Arbiters - Bus

  4. Bit-Sliced Design

  5. Full-Adder

  6. The Binary Adder

  7. Express Sum and Carry as a function of P, G, D

  8. The Ripple-Carry Adder

  9. Complimentary Static CMOS Full Adder

  10. Inversion Property

  11. Minimize Critical Path by Reducing Inverting Stages

  12. The better structure: the Mirror Adder

  13. The Mirror Adder • The NMOS and PMOS chains are completely symmetrical. This guarantees identical rising and falling transitions if the NMOS and PMOS devices are properly sized. A maximum of two series transistors can be observed in the carry-generation circuitry. • When laying out the cell, the most critical issue is the minimization of the capacitance at node Co. The reduction of the diffusion capacitances is particularly important. • The capacitance at node Co is composed of four diffusion capacitances, two internal gate capacitances, and six gate capacitances in the connecting adder cell . • The transistors connected to Ci are placed closest to the output. • Only the transistors in the carry stage have to be optimized for optimal speed. All transistors in the sum stage can be minimal size.

  14. Quasi-Clocked Adder

  15. NMOS-Only Pass Transistor Logic

  16. NP-CMOS Adder

  17. NP-CMOS Adder C o1 S 1 A 1 B 1 S 0 A 0 B 0 C i0

  18. Manchester Carry Chain

  19. Sizing Manchester Carry Chain

  20. Carry-Bypass Adder

  21. Manchester-Carry Implementation

  22. Carry-Bypass Adder (cont.)

  23. Carry Ripple versus Carry Bypass

  24. Carry-Select Adder

  25. Carry Select Adder: Critical Path

  26. Linear Carry Select

  27. Square Root Carry Select

  28. Adder Delays - Comparison

  29. LookAhead - Basic Idea

  30. Look-Ahead: Topology

  31. Logarithmic Look-Ahead Adder

  32. Brent-Kung Adder

  33. The Binary Multiplication

  34. The Binary Multiplication

  35. The Array Multiplier

  36. The MxN Array Multiplier— Critical Path Critical Path 1 & 2

  37. Carry-Save Multiplier

  38. Adder Cells in Array Multiplier

  39. Multiplier Floorplan

  40. Wallace-Tree Multiplier

  41. Multipliers —Summary

  42. Design as a Trade-Off

  43. Layout Strategies for Bit-Sliced Datapaths

  44. Layout of Bit-sliced Datapaths

  45. Layout of Bit-sliced Datapaths