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**Chapter 7 Virtex Arithmetic Structures**

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Overview Addition and subtraction Multiplication DSP48 DSP48E

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**Ci+1 = Ai Bi + (Ai XOR Bi) Ci**

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

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Basic Ripple Adder

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Fast Carry Chains Bi Ai COUT CIN LUT Si 1

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Tracing Carry Chain

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**Counters Built from Adders**

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**Multiplication Review**

A3A2A1A0 X B1B0 A3B0 A2 B0 A1B0 A0B0 A3B A2B1 A1 B1 A0 B1 P P P P P P0 Just like in the third grade . . .

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**Fabric Based Multiplier**

(comment: should be COUT)

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**Mult/AND Identification**

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**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

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**Virtex II/Spartan 3/E Block Multipliers**

Combinational 2’s Complement Sequential 2’s Complement

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**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

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22 X 16 Bit Multiplier Fabric Block Fabric

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**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

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**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

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Two Slice DSP 48 Top Slice Bottom Slice

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**Simplified DSP 48 Adder Out = Z +/- (X + Y + CIN)**

Adder Out = C +/- (A X B + CIN)

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**The DSP 48 Instruction Set**

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DSP 48 Primitive Symbol

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DSP 48 Timing

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**Doing Other Things - SQRT**

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**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

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Virtex 5 DSP48E

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Simpler DSP48E

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**Other Useful Functions**

Building up “word wise” logic AND,OR Same list as for the DSP48

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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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1 Lecture 12: Hardware for Arithmetic Today’s topics: Designing an ALU Carry-lookahead adder Reminder: Assignment 5 will be posted in a couple of days.

1 Lecture 12: Hardware for Arithmetic Today’s topics: Designing an ALU Carry-lookahead adder Reminder: Assignment 5 will be posted in a couple of days.

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