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ECE 555 Digital Circuits & Components ECE555 Lecture 10 Nam Sung Kim University of Wisconsin – Madison Dept. of Electrical & Computer Engineering 1.

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Presentation on theme: "ECE 555 Digital Circuits & Components ECE555 Lecture 10 Nam Sung Kim University of Wisconsin – Madison Dept. of Electrical & Computer Engineering 1."— Presentation transcript:

1 ECE 555 Digital Circuits & Components ECE555 Lecture 10 Nam Sung Kim University of Wisconsin – Madison Dept. of Electrical & Computer Engineering 1

2 ECE 555 Digital Circuits & Components Outline Multiplier Array Multiplier CSA/Wallace Tree Multiplier Shifter Datapath Bitslice Organization 2

3 ECE 555 Digital Circuits & Components Multiplication Example 3

4 ECE 555 Digital Circuits & Components Multiplication Example 4

5 ECE 555 Digital Circuits & Components Multiplication Example 5

6 ECE 555 Digital Circuits & Components Multiplication Example 6

7 ECE 555 Digital Circuits & Components Multiplication Example 7

8 ECE 555 Digital Circuits & Components Multiplication Example 8

9 ECE 555 Digital Circuits & Components Multiplication Example M x N-bit multiplication Produce N M-bit partial products Sum these to produce M+N-bit product 9

10 ECE 555 Digital Circuits & Components General Multiplication Form Multiplicand: Y = (y M-1, y M-2, …, y 1, y 0 ) Multiplier: X = (x N-1, x N-2, …, x 1, x 0 ) Product: 10

11 ECE 555 Digital Circuits & Components Dot Diagram Each dot represents a bit (or partial product) 11

12 ECE 555 Digital Circuits & Components Array Multiplier 12

13 ECE 555 Digital Circuits & Components Rectangular Array Squash array to fit rectangular floorplan 13

14 ECE 555 Digital Circuits & Components Wallace Tree Multiplier Using 3:2 compressor (FA!) x0x0 x3x3

15 ECE 555 Digital Circuits & Components Wallace Tree Multiplier Using 3:2 compressor (FA!) x0y0x0y0 x0y1x0y1 x0y2x0y2 x0y3x0y3 x1y0x1y0 x1y1x1y1 x1y2x1y2 x1y3x1y3 x2y0x2y0 x2y1x2y1 x2y2x2y2 x2y3x2y3 x3y0x3y0 x3y1x3y1 x3y2x3y2 x3y3x3y3 ++ +

16 ECE 555 Digital Circuits & Components Wallace Tree Multiplier Using 3:2 compressor (FA!) x0y0x0y0 x0y1x0y1 x0y2x0y2 x0y3x0y3 x1y0x1y0 x1y1x1y1 x1y2x1y2 x1y3x1y3 x2y0x2y0 x2y1x2y1 x2y2x2y2 x3y0x3y0 x3y1x3y1 x3y3x3y x2y3x2y3 x3y2x3y2 + +

17 ECE 555 Digital Circuits & Components Wallace Tree Multiplier 17

18 ECE 555 Digital Circuits & Components Parallel Programmable Shifters Data In Control = Data Out Shift amount Shift direction Shift type (logical, arith, circular) Shifters used in multipliers, floating point units Consume lots of area if done in random logic gates

19 ECE 555 Digital Circuits & Components A Programmable Binary Shifter rgtnopleft AiAi A i-1 B i-1 BiBi AiAi A i-1 rgtnopleftBiBi B i-1 A1A1 A0A0 010A1A1 A0A0 A1A1 A0A0 1000A1A1 A1A1 A0A0 001A0A0 0

20 ECE 555 Digital Circuits & Components A Programmable Binary Shifter rgtnopleft AiAi A i-1 B i-1 BiBi AiAi A i-1 rgtnopleftBiBi B i-1 A1A1 A0A0 010A1A1 A0A0 A1A1 A0A0 1000A1A1 A1A1 A0A0 001A0A0 0

21 ECE 555 Digital Circuits & Components 4-bit Barrel Shifter A0A0 A1A1 A2A2 A3A3 B0B0 B1B1 B2B2 B3B3 Sh1 Sh2 Sh3 Sh0Sh1Sh2Sh3 Example: Sh0 = 1 B 3 B 2 B 1 B 0 = A 3 A 2 A 1 A 0 Sh1 = 1 B 3 B 2 B 1 B 0 = A 3 A 3 A 2 A 1 Sh2 = 1 B 3 B 2 B 1 B 0 = A 3 A 3 A 3 A 2 Sh3 = 1 B 3 B 2 B 1 B 0 = A 3 A 3 A 3 A 3 Area dominated by wiring

22 ECE 555 Digital Circuits & Components 4-bit Barrel Shifter A0A0 A1A1 A2A2 A3A3 B0B0 B1B1 B2B2 B3B3 Sh1 Sh2 Sh3 Sh0Sh1Sh2Sh3 Example: Sh0 = 1 B 3 B 2 B 1 B 0 = A 3 A 2 A 1 A 0 Sh1 = 1 B 3 B 2 B 1 B 0 = A 3 A 3 A 2 A 1 Sh2 = 1 B 3 B 2 B 1 B 0 = A 3 A 3 A 3 A 2 Sh3 = 1 B 3 B 2 B 1 B 0 = A 3 A 3 A 3 A 3 Area dominated by wiring

23 ECE 555 Digital Circuits & Components 4-bit Barrel Shifter Layout Width barrel ~ 2 p m N N = max shift distance, p m = metal pitch Delay ~ 1 fet + N diff caps Width barrel Only one Sh# active at a time l

24 ECE 555 Digital Circuits & Components 8-bit Logarithmic Shifter A3A3 A2A2 A1A1 A0A0 !Sh1Sh1!Sh2Sh2!Sh3Sh3 B0B0 B1B1 B2B2 B3B3

25 ECE 555 Digital Circuits & Components 8-bit Logarithmic Shifter A3A3 A2A2 A1A1 A0A0 !Sh1Sh1!Sh2Sh2!Sh3Sh3 B0B0 B1B1 B2B2 B3B3 log N stages

26 ECE 555 Digital Circuits & Components 8-bit Logarithmic Shifter Layout Width log ~ p m (2K+(1+2+…+2 K-1 )) = p m (2 K +2K-1) K = log 2 N Delay ~ K fets + 2 diff caps A0A0 B3B3 B2B2 B1B1 B0B0 A1A1 A2A2 A3A3 124

27 ECE 555 Digital Circuits & Components Datapath Bit-Sliced Organization 27 Control Flow Bit 0 Bit 1 Bit 2 Bit 3 Tile identical bit-slice elements Register File Pipeline RegisterAdderShifterPipeline RegisterMultiplexer Data Flow Pipeline Register From I$ Pipeline Register To/From D$ decoder


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