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### Binary conversion, with fixed decimal precision, of a decimal fraction

Donald Taranto
1959 Communications of the ACM
Tg —_ 2 7 2 Qe ee a Binary Conversion, With Fixed Decimal Precision, Of a Decimal Fraction Donatp Taranto, International Business Machines Corp., New York, N.Y.  ...  Problem Given a decimal fraction f, find a binary approximation f, to f, with a given decimal precision h. 1. Given O Sf < Llandh > 0. 2. Find f, such that | f — f,| Sh.  ...

### How to print floating-point numbers accurately

Guy L. Steele, Jon L. White
1990 SIGPLAN notices
(The problem of binary-to-decimal conversion is amazingly tricky, even for fixed-point fractions, let alone floatingpoint numbers [31][22][20] [12] .)  ...  to print out with too many decimal digits.  ...  (The problem of binary-to-decimal conversion is amazingly tricky, even for fixed-point fractions, let alone floatingpoint numbers [31] [22] [20] [12] .)  ...

### How to print floating-point numbers accurately

Guy L. Steele, Jon L. White
2004 SIGPLAN notices
(The problem of binary-to-decimal conversion is amazingly tricky, even for fixed-point fractions, let alone floatingpoint numbers [31][22][20] [12] .)  ...  to print out with too many decimal digits.  ...  (The problem of binary-to-decimal conversion is amazingly tricky, even for fixed-point fractions, let alone floatingpoint numbers [31] [22] [20] [12] .)  ...

### How to print floating-point numbers accurately

Guy L. Steele, Jon L. White
1990 Proceedings of the ACM SIGPLAN 1990 conference on Programming language design and implementation - PLDI '90
(The problem of binary-to-decimal conversion is amazingly tricky, even for fixed-point fractions, let alone floatingpoint numbers [31][22][20] [12] .)  ...  to print out with too many decimal digits.  ...  (The problem of binary-to-decimal conversion is amazingly tricky, even for fixed-point fractions, let alone floatingpoint numbers [31] [22] [20] [12] .)  ...

### EARLY ESTIMATION OF DELAY IN BINARY TO BCD CONVERTOR

D. JOTHSNA NARSIMHAM, P. LAKSHMI SAROJINI
2014 International Journal of Electronics and Electical Engineering
A novel high speed architecture for fixed bit binary to BCD conversion which is better in terms of delay is presented in this paper.  ...  Decimal digit multipliers are having Binary to BCD conversion as the basic building block.  ...  Rational numbers whose denominator is a power of ten are decimal fractions and most them cannot be represented by binary fractions.  ...

### Page 27 of Communications of the Association for Computing Machinery Vol. 2, Issue 7 [page]

1959 Communications of the Association for Computing Machinery
Tg —_ 2 7 2 Qe ee a Binary Conversion, With Fixed Decimal Precision, Of a Decimal Fraction Donatp Taranto, International Business Machines Corp., New York, N.Y.  ...  Problem Given a decimal fraction f, find a binary approximation f, to f, with a given decimal precision h. 1. Given O Sf < Llandh > 0. 2. Find f, such that | f — f,| Sh.  ...

### Proposal for a High Precision Tensor Processing Unit [article]

Eric B. Olsen
2017 arXiv   pre-print
This whitepaper proposes the design and adoption of a new generation of Tensor Processing Unit which has the performance of Google's TPU, yet performs operations on wide precision data.  ...  The new generation TPU is made possible by implementing arithmetic circuits which compute using a new general purpose, fractional arithmetic based on the residue number system.  ...  RNS conversion, and fractional RNS to fractional binary conversion.  ...

### Radix conversion in an unnormalized arithmetic system

N. Metropolis, R. L. Ashenhurst
1965 Mathematics of Computation
The observation that the exact conversion of integers gives also a true estimate of precision (i.e., the 10-for-3 criterion is naturally achieved), suggests that binary-decimal conversion can be accomplished  ...  It seems not unreasonable, however, to ask for a conversion procedure which affords the user a more precise statement of the relation between the binary form and the decimal result.  ...  This stage is therefore skipped, and the integer d0 is determined from the fractional part of the initial product. Decimal-Binary Conversion.  ...

### Performance analysis of decimal floating-point libraries and its impact on decimal hardware and software solutions

J. Michael Anderson, Charles Tsen, Liang-Kai Wang, Katherine Compton, J. Michael Schulte
2009 2009 IEEE International Conference on Computer Design
A growing number of DFP solutions have emerged, and developers now have many DFP design choices including arbitrary or fixed precision, binary or decimal significand encodings, 64-bit or 128-bit DFP operands  ...  DFP operation in each benchmark, and (3) highlights the tradeoffs between using 64-bit and 128-bit DFP operands for both binary and decimal significand encodings.  ...  For example, the binary floating-point (BFP) single-precision number closest to the decimal fraction 0.1 is actually equal to 0.100000001490116119384765625.  ...

### Functions to Support Input and Output of Intervals [article]

M.H. van Emden, B. Moa, S.C. Somosan
2007 arXiv   pre-print
Equally essential for interval methods is directed rounding for conversion between the external decimal and internal binary numerals. This is not provided by the standard I/O libraries.  ...  Although it may be possible to adapt these algorithms for use in decimal interval I/O, we argue that outward rounding in radix conversion is computationally a simpler problem than guaranteeing identity  ...  Acknowledgements This research was supported by the University of Victoria and by the Natural Science and Engineering Research Council of Canada.  ...

### A new math library

Nelson H. F. Beebe
2009 International Journal of Quantum Chemistry
many digits: more than 11 500 decimal digits for binary-to-decimal conversion of 128-bit format, J base-conversion problem not properly solved until 1990s J few (if any) languages guarantee accurate base  ...  J for a fixed number of exponent digits, larger bases provide a wider exponent range, and reduce incidence of rounding J for a fixed storage size, granularity (the spacing between successive representable  ...  Beebe (University of Utah) MAA/BYU: A new math library / 25 / 25  ...

### The Programming Algorithm Based on Embedded System for the Output Conversion of the Humidity & Temperature Sensor SHTxx

Jiu Peng Zou, Yu Qiang Dai, Xue Wu Liu, Li Ming Zhang, Feng Xia Liu
2012 Advanced Engineering Forum
The polynomials are precise equivalent to the conversion formulas provided by the manufacturers, but contain only Binary fixed-point integer, fractional part, and 2N.  ...  In order to avoid the digital humidity & temperature sensor SHTxx's output values conversion consume many quantity of storage location, and spend more operation time, a group new type of conversion polynomials  ...  integer and binary fractional part, so the item can be calculated with fixed-point addition and subtraction, the conversion error of fractional part relative to the quondam formula (1) is only 1.5‰.  ...

### Page 318 of Mathematics of Computation Vol. 3, Issue 24 [page]

1948 Mathematics of Computation
The conversion to binary should be no more difficult than the conversion to decimal. For control purposes it may be required to convert the output of the computer back into continuous form.  ...  Many machines are provided with equipment for operating at two different precisionsa low precision which is usually standard, and a high precision, double the low one, which is the less frequently employed  ...

### On Basic Financial Decimal Operations on Binary Machines

Abhilasha Aswal, Ganesh Perumal, G.N. Srinivasa Prasanna Prasanna
2012 IEEE transactions on computers
In addition, we describe methods for correctly performing basic decimal operations, such as addition, subtraction, multiplication, and division, on binary machines, which are not conformant with IEEE 754  ...  In this paper, we show that if binary arithmetic is used to emulate decimal operations, then arbitrary error sequences can be generated by carefully chosen sequences of transactions which can lead to monotonically  ...  The ideas can be analogously extended for 34 digits of precision, but will come with a conversion overhead.  ...

### A Software Implementation of the IEEE 754R Decimal Floating-Point Arithmetic Using the Binary Encoding Format

Marius Cornea, Cristina Anderson, John Harrison, Ping Tak Peter Tang, Eric Schneider, Charles Tsen
2007 Computer Arithmetic
New algorithms and properties are presented in this paper which are used in a software implementation of the IEEE 754R decimal floatingpoint arithmetic, with emphasis on using binary operations efficiently  ...  This is intended mainly to provide a robust, reliable framework for financial applications that are often subject to legal requirements concerning rounding and precision of the results, because the binary  ...  Conversion from Double Precision to 64-bit Decimal The double precision argument encodes the value a = (−1) sa · 2 ea · m a = (−1) sa · 2 k · C a , with C a an integer in the range [0, 2 53 ) and k an  ...
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