An architecture for addition and subtraction of long word length numbers in the logarithmic number system

1990 ◽  
Vol 39 (11) ◽  
pp. 1325-1336 ◽  
Author(s):  
D.M. Lewis
Keyword(s):  
Word Length ◽  
Number System ◽  
Logarithmic Number System ◽  
Addition And Subtraction ◽  
Logarithmic Number

scholarly journals Less memory and high accuracy logarithmic number system architecture for arithmetic operations

2021 ◽  
Vol 23 (3) ◽  
pp. 1708
Author(s):  
Siti Zarina Md Naziri ◽  
Rizalafande Che Ismail ◽  
Mohd Nazrin Md Isa ◽  
Razaidi Hussin
Keyword(s):  
Number System ◽  
Memory Consumption ◽  
Logarithmic Number System ◽  
Extended Range ◽  
Interpolation Procedure ◽  
Proper Design ◽  
Addition And Subtraction ◽  
Operation Results ◽  
Logarithmic Number ◽  
Second Degree

<p>Interpolation is another important procedure for logarithmic number system (LNS) addition and subtraction. As a medium of approximation, the interpolation procedure has an urgent need to be enhanced to increase the accuracy of the operation results. Previously, most of the interpolation procedures utilized the first degree interpolators with special error correction procedure which aim to eliminate additional embedded multiplications. However, the interpolation procedure for this research was elevated up to a second degree interpolation. Proper design process, investigation, and analysis were done for these interpolation configurations in positive region by standardizing the same co-transformation procedure, which is the extended range, second order co-transformation. Newton divided differences turned out to be the best interpolator for second degree implementation of LNS addition and subtraction, with the best-achieved BTFP rate of +0.4514 and reduction of memory consumption compared to the same arithmetic used in european logarithmic microprocessor (ELM) up to 51%.</p>

scholarly journals Design of Finite Word Length Linear-Phase FIR Filters in the Logarithmic Number System Domain

VLSI Design ◽  
2014 ◽  
Vol 2014 ◽  
pp. 1-14 ◽  
Author(s):  
Syed Asad Alam ◽  
Oscar Gustafsson
Keyword(s):  
Word Length ◽  
Approximation Error ◽  
Number System ◽  
Fir Filters ◽  
Attractive Alternative ◽  
Logarithmic Number System ◽  
Finite Word Length ◽  
Finite Word ◽  
Impulse Response Filters ◽  
Logarithmic Number

Logarithmic number system (LNS) is an attractive alternative to realize finite-length impulse response filters because of multiplication in the linear domain being only addition in the logarithmic domain. In the literature, linear coefficients are directly replaced by the logarithmic equivalent. In this paper, an approach to directly optimize the finite word length coefficients in the LNS domain is proposed. This branch and bound algorithm is implemented based on LNS integers and several different branching strategies are proposed and evaluated. Optimal coefficients in the minimax sense are obtained and compared with the traditional finite word length representation in the linear domain as well as using rounding. Results show that the proposed method naturally provides smaller approximation error compared to rounding. Furthermore, they provide insights into finite word length properties of FIR filters coefficients in the LNS domain and show that LNS FIR filters typically provide a better approximation error compared to a standard FIR filter.

scholarly journals Hybrid Floating Point/Logarithmic Number System Processor

2020 ◽  
Vol 932 ◽  
pp. 012059
Author(s):  
C Y Sheng ◽  
R C Ismail ◽  
S Z M Naziri ◽  
M N M Isa ◽  
S A Z Murad ◽  
...  
Keyword(s):  
Number System ◽  
Floating Point ◽  
Logarithmic Number System ◽  
Logarithmic Number

Implementing the Residue Logarithmic Number System Using Interpolation and Cotransformation

2020 ◽  
Vol 69 (12) ◽  
pp. 1719-1732 ◽  
Author(s):  
Mark G. Arnold ◽  
Vassilis Paliouras ◽  
Ioannis Kouretas
Keyword(s):  
Number System ◽  
Logarithmic Number System ◽  
Logarithmic Number
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