A 16-Bit Kogge Stone PS-CMOS adder with Signal Completion

Seng-Oon Toh, Daniel Huang, Jan RabaeyMay 9, 2005

EE241 Final Project

May 9, 2005 2EE241

Motivation

Asynchronous designs give better throughput and has higher efficiency

Larger circuits and smaller transistors is more susceptible to process variations.

Process variation decreases yield of circuits Reach optimum clocking frequency per block Need for self timing with the circuits with a signal

completion, which also increases yield from process variations.

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Past Solution

GALS DCDVSL

IEEE, 1998

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PS-CMOS 16-bit Kogge-Stone Pipelined Adder

Adders– Adder is an integral

part of ALU– Large pipelined adders

may be beneficial for large adders to increase clock frequencies and throughput

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PS-CMOS 16-bit Kogge Stone Pipelined Adder

Adder Design– Kogge-Stone CLA– Four stages

» Stage 1: Bit P and G» Stage 2: Dot 1, 2» Stage 3: Dot 3, 4, Cout» Stage 4: Sum

– 2-Input gates, no complex logic gates, for significant logic depth.

1

2

3

4

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PS-CMOS 16-bit Kogge Stone Pipelined Adder

PS-CMOS– Monotonic output transition– Noise Immunity– Pseudo-dynamic, fast evaluate

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PS-CMOS 16-bit Kogge Stone Pipelined Adder

Completion Signal– Simple scheme that is compatible with PS-

CMOS» DCDVSL» Dummy paths

– Take advantage of monotonic output transition– Input the worst case input vector upon startup

to find clock frequency– Calibrate in situ

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Completion Signal Scheme

Output signal

Clock signal

Delay Output signal

precharge

evaluate

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Completion Signal Scheme Slow Clock

Output signal

Clock signal

Delay Output signal

precharge

evaluate

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Completion Signal SchemeFast Clock

Output signal

Clock signal

Delay Output signal

precharge

evaluate

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Completion Signal Circuitry

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Completion Signal Circuitry

Input OutputCritical path

Input check

sum

Check for delay Increase, decrease, stop counting

8-bit Counter

VCOClock Generation

DAC

Stage 3

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Results

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Results

Supply Voltage Scaling

0.60.70.80.91

1.11.21.31.4

1 1.2 1.4 1.6 1.8 2 2.2

Vdd (V)

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Results

Theoretical delay 714ps, measure 850ps For in situ calibration how often will the worst

case input vector appear?– Assuming perfectly random inputs– Worst case input vector will appear approximately once

every 105 switches– Circuit runs approximately 109 switches per second– Every second there can be a potential of 104 updates.– This sets the optimum clock speed to clock for the

calibration circuitry

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Results

Counter able to count up as well as down– Speed up and slow down based on conditions

Ability to calibrate for different supply voltages

Ability to test at startup and in situ

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Discussion

Ideal sensor has 0 capacitance– We have small capacitance– 1 inverter, 1 latch

Circuit Overhead low Probability of Switching

– Maximum clock frequency for test circuit– Calibration frequency is high– Multiple paths available for detection

Closes feedback path for DVS

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Discussion During clock change no evaluation is allowed Slack margin 100 ps built in delay from detection

– Nonexistant with registers, because of intrinsic need of delay for registers

PS-CMOS– Difficult to implement XOR– Not straight forward logic– When used with latches timing of precharge and evaluate

is difficult Frequency increments

– Small time step necessary for stability

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Future Improvements

Fix delay overhead of detection circuit Fix problems from latch based design Circuitry for multiple path detection Super Pipeline 256-bit adder Ability to run adder slower

– Monitor precharge

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Conclusion Shown a simple completion signal scheme

for a pipelined PS-CMOS adder Small amount of overhead Ability to adjust clock frequencies during

operation not only on startup

Because I could not stop for Death,He kindly stopped for me;The carriage held but just ourselvesAnd Immortality.

-Emily Dickinson, 1924