Issue No. 11 - November (2003 vol. 52)

ISSN: 0018-9340

pp: 1421-1433

Khalid H. Abed , IEEE

Raymond E. Siferd , IEEE

ABSTRACT

<p><b>Abstract</b>—This paper presents a unique 32-bit binary-to-binary logarithm converter including its CMOS VLSI implementation. The converter is implemented using combinational logic only and it calculates a logarithm approximation in a single clock cycle. Unlike other complex logarithm correcting algorithms, three unique algorithms are developed and implemented with low-power and fast circuits that reduce the maximum percent errors that result from binary-to-binary logarithm conversion to 0.9299 percent, 0.4314 percent, and 0.1538 percent. Fast 4, 16, and 32-bit leading-one detector circuits are designed to obtain the leading-one position of an input binary word. A 32-word x 5-bit MOS ROM is used to provide 5-bit integers based on the corresponding leading-one position. Both converter area and speed have been considered in the design approach, resulting in the use of a very efficient 32-bit logarithmic shifter in the 32--bit logarithmic converter. The converter is implemented using <tmath>0.6\mu{\rm m}</tmath> CMOS technology, and it requires <tmath>1,600\lambda\times 2,800\lambda</tmath> of chip area. Simulations of the CMOS design for the 32-bit logarithmic converter, operating at <tmath>{\rm V_{DD}}</tmath> equal to 5 volts, run at 55 MHz, and the converter consumes 20 milliwatts.</p>

INDEX TERMS

Anti-logarithm, binary logarithms, elementary functions, floating-point normalization, logarithmic number system, leading-one detector, low-power circuits.

CITATION

Khalid H. Abed, Raymond E. Siferd, "CMOS VLSI Implementation of a Low-Power Logarithmic Converter",

*IEEE Transactions on Computers*, vol. 52, no. , pp. 1421-1433, November 2003, doi:10.1109/TC.2003.1244940