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Overview of Virtex Arithmetic Structures: Addition, Multiplication, and DSP48 Applications

This chapter provides an in-depth overview of Virtex arithmetic structures, focusing on fundamental operations such as addition, subtraction, and multiplication. It details essential components like the DSP48 and DSP48E, including basic adder equations and fast carry chains. The chapter also explores block multipliers in Xilinx Spartan 3/E and Virtex II, and discusses their applications, efficiencies, and alternative uses. Furthermore, it highlights the advanced features of DSP48, designed for efficient cascading and integrating complex arithmetic operations, supporting a wide array of DSP applications.

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Overview of Virtex Arithmetic Structures: Addition, Multiplication, and DSP48 Applications

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  1. Chapter 7 Virtex Arithmetic Structures

  2. Overview • Addition and subtraction • Multiplication • DSP48 • DSP48E

  3. Basic Adder Equations Si = Ai XOR Bi XOR Ci Ci+1 = Ai Bi + (Ai XOR Bi) Ci Note: not unique expression for Ci+1

  4. Basic Ripple Adder

  5. COUT LUT 0 1 Bi Si Ai CIN Fast Carry Chains

  6. Tracing Carry Chain

  7. Counters Built from Adders

  8. Multiplication Review A3A2A1A0 X B1B0 ------------------------------------------------- A3B0 A2 B0 A1B0 A0B0 A3B1 A2B1 A1 B1 A0 B1 ------------------------------------------------- P5 P4 P3 P2 P1 P0 Just like in the third grade . . .

  9. Fabric Based Multiplier (comment: should be COUT)

  10. Mult/AND Identification

  11. Block Multipliers • Xilinx Spartan 3/E and Virtex II = 18 bit • Applications needing fewer bits can tie off higher order bits appropriately • Applications needing more bits must either: • Cascade block multipliers • Combine blocks with fabric multipliers • Other uses for block multipliers

  12. Virtex II/Spartan 3/E Block Multipliers Combinational 2’s Complement Sequential 2’s Complement

  13. Spartan 3 Multiplier Mix With this many multipliers, better be something we can do with them if we Don’t need this many. Also, must be other sizes we can create – somehow. See XAPP 467

  14. 22 X 16 Bit Multiplier Fabric Block Fabric

  15. Other Uses • Multiply several small numbers with one block multiplier • Division by repeated multiplication • Barrel shift using multiplier • Take two’s complement of a number • Get the magnitude of a two’s complement number • There are others

  16. DSP 48 • Introduced for Virtex 4 • Designed to efficiently cascade • Xilinx teamed with outside arithmetic specialists to get best speed/area blocks • Supports multiple rounding formats • Not present in all V4 families

  17. Two Slice DSP 48 Top Slice Bottom Slice

  18. Simplified DSP 48 Adder Out = Z +/- (X + Y + CIN) Adder Out = C +/- (A X B + CIN)

  19. The DSP 48 Instruction Set

  20. DSP 48 Primitive Symbol

  21. DSP 48 Timing

  22. Doing Other Things - SQRT

  23. Important to Do Other Things with DSP 48 • Divider • Large multiplexer • Barrel shifters • Two’s Complement converters • Large counters • Etc. DSP 48 Handbook available on Xilinx website

  24. Virtex 5 DSP48E

  25. Simpler DSP48E

  26. Other Useful Functions • Building up “word wise” logic • AND,OR • Same list as for the DSP48

  27. Support • Xilinx offers an elaborate (read:$) set of tools that interface to the MatLab toolchain • Focused on DSP algorithm development • Permits “hardware in the loop” simulation • Also working on higher level compile tools as DSP developers tend to be more mathematicians and less “hardware designers” (read: C, C++ oriented)

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