elec 5270 low power design of electronic circuits spring 2009 n.
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ELEC 5270 – Low Power Design of Electronic Circuits Spring 2009. Binary Counter with Decimal and Gray Encoding. Grant Lewis. Decimal Encoding. 3-bit Counter has 14 transitions in 8 cycles 14/8 = 1.75 transitions per cycle N-bit Counter has 2(2 N -1) transitions

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decimal encoding
Decimal Encoding
  • 3-bit Counter has 14 transitions in 8 cycles
    • 14/8 = 1.75 transitions per cycle
  • N-bit Counter has 2(2N-1) transitions
    • Transitions per cycle → 2 as N→ ∞

4-bit 1.875 transitions/clock

5-bit 1.9375

6-bit 1.96875

7-bit 1.984375

8-bit 1.9921875

9-bit 1.99609375

decimal encoding1
Decimal Encoding
  • A =
  • B =
  • C =
  • 8 logic gates

Synthesize in Leonardo Spectrum

gray encoding
Gray Encoding
  • 3-bit counter has 8 transitions in 8 cycles
    • 8/8 = 1 transition per cycle
  • N-bit counter has 2N transitions
    • Transitions per cycle is 1 for any size counter
  • For large counters, ratio of transitions for Decimal to Gray → 2
gray encoding1
Gray Encoding
  • Gray Encoding can be accomplished by
    • Binary to Gray conversion
    • Directly Synthesizing Gray Counter
  • Binary to Gray conversion is accomplished with 2 XOR gates
binary to gray conversion
Binary to Gray Conversion
  • With optimizations, adds one logic gate (total 9 logic gates)
gray encoding2
Gray Encoding
  • A =
  • B =
  • C =
  • Adds 4 logic gates (total 12 gates)
power analysis
Power Analysis
  • Power analysis conducted with powersim

.18 μm, 1.8V supply

conclusions
Conclusions
  • Much of dynamic power consumption comes from glitches
    • Can be reduced by path balancing
  • Directly implementing gray counter in logic removes ~1/2 of the glitches, however consumes more leakage and logic power due to increase in number of logic gates
  • Overall, gray counters are more power efficient
references
References
  • Hakenes, R.; Manoli Y. “A Segmented Gray Code for Low-Power Microcontroller Address Buses”. EUROMICRO Conference, 1999. Proceedings. 25th, Pages 240 – 243, Vol. 1
  • Doran, R. W. “The Gray Code”. Centre for Discrete Mathematics and Theoretical Computer Science, March, 2007.
  • Mehta, Huzefa et al. “Some Issues in Gray Code Addressing”. Proceedings of the 6th Great Lakes Symposium on VLSI, 1996. Pages 178 – 181.