# \[1959\] The residue number system
**URL:** https://collective.flashbots.net/t/1959-the-residue-number-system/6023
**Category:** References
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**Created:** [September 14, 2026, 10:34am UTC](https://collective.flashbots.net/t/1959-the-residue-number-system/6023 "2026-09-14T10:34:23Z")
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### Author:  [@guayabyte](https://collective.flashbots.net/u/guayabyte)
#### Post date: [September 14, 2026, 10:34am UTC](https://collective.flashbots.net/t/1959-the-residue-number-system/6023/1 "2026-09-14T10:34:23Z")
Abstract: n this paper we develop and investigate the properrties of a novel system, called the residue code or residue number system. The residue number system is of particular interest because the arithmetic operations of addition and multiplication may be executed in the same time as required for an addition operation. The main difficulty of the residue code relative to arithmetic operations is the determination of the relative magnitude of two numbers expressed in the residue code. The residue code is probably of little utility for general-purpose computation, but the code has many characteristics which recommend its use for special-purpose computations.
```auto
@inproceedings{10.1145/1457838.1457864,
author = {Garner, Harvey L.},
title = {The residue number system},
year = {1959},
isbn = {9781450378659},
publisher = {Association for Computing Machinery},
address = {New York, NY, USA},
url = {https://doi.org/10.1145/1457838.1457864},
doi = {10.1145/1457838.1457864},
abstract = {In this paper we develop and investigate the properrties of a novel system, called the residue code or residue number system. The residue number system is of particular interest because the arithmetic operations of addition and multiplication may be executed in the same time as required for an addition operation. The main difficulty of the residue code relative to arithmetic operations is the determination of the relative magnitude of two numbers expressed in the residue code. The residue code is probably of little utility for general-purpose computation, but the code has many characteristics which recommend its use for special-purpose computations.},
booktitle = {Papers Presented at the the March 3-5, 1959, Western Joint Computer Conference},
pages = {146–153},
numpages = {8},
location = {San Francisco, California},
series = {IRE-AIEE-ACM '59 (Western)}
}
```
[https://doi.org/10.1145/1457838.1457864](https://doi.org/10.1145/1457838.1457864)
---
### Author:  [@guayabyte](https://collective.flashbots.net/u/guayabyte)
#### Post date: [September 14, 2026, 10:34am UTC](https://collective.flashbots.net/t/1959-the-residue-number-system/6023/2 "2026-09-14T10:34:47Z")
My highlights: [ceibita-papers : Free Download, Borrow, and Streaming : Internet Archive](https://archive.org/details/ceibita-papers/1959-the_residue_number_system_annotated.pdf)