1. 16 Bit Logarithmic Converter Tinghao Liang and Sara Nadeau

2. 16 Bit Logarithmic Converter • Introduction • Motivation • Algorithm Explanation • High level description • Block diagram • Design strategy • Baseline performance • Performance goals • Improvement strategy • Improved performance • Layout • Conclusions and Future Work

3. Project Motivation • Logarithmic converters simplify computational needs • Multiplication/Division -> Addition/Subtraction • Power/Root -> Multiplication/Division • Real time DSP becoming more and more in demand, increased need for log converters to simplify computation demands • Explore interesting circuitry

4. Algorithm • Whole number portion of base two logarithm of binary input acquired by detecting leading 1 • Decimal portion of base two logarithm of binary input approximated by mantissa • Ex: Input -> 2910 or 111012 Binary answer -> 100.1101 Decimal answer -> 4.8579 Error -> 0.0454, or 0.9%

5. Implementation – Block Diagram

6. Baseline Design Strategy • Direct CMOS implementation of all circuit blocks • Use gates sized for matching rise and fall times from lab 2 • Goal – functional circuitry

7. Implementation – Leading One Detector Functionality LOD4 LOD16

8. Implementation – ROM Functionality

9. Implementation – Barrel Shifter Functionality

10. Baseline Design Results • 50 MHz operation speed • 5 mW power consumption

11. Improvement Strategy - Speed • Critical path • MSB’s pass through LOD and ROM prior to output • LSB’s need valid ROM output before barrel shifter output is valid • Critical block – 2:1 MUX • Appears in LOD as well as barrel shifter, often cascaded • Sized with logical effort • 4-Input NOR also resized for minimum average delay

12. Improvement Strategy - Power • Power supply reduced to 2 V • Circuitry simplified • ROM circuit activated only when clock is low

13. Improvement Strategy - Functionality • Expanded from 8 bits to 16 bits • Added a flag to indicate zero input

14. Schematic Changes - MUX

15. Improved Design Results • 77 MHz operation speed • 1.7 mW power consumption

16. Layout – Register

17. Layout – Leading One Detector

18. Layout - ROM

19. Layout – Barrel Shifter

20. Improved Design Layout

21. Improved Design Layout

22. Conclusions and Future Work • Conclusions • Functional base two log converter designed and simulated successfully • Speed and power consumption were both improved by design modifications • Improvements • Size ROM cell for better speed • Further optimize layout organization • Add error compensation circuitry • Build anti-logarithmic converter

23. Thank you! • Questions?