Number Representation With Varying Number of Bits

Authors

Anuradha Choudhury, The University of Texas at El PasoFollow
Md Ahsanul Haque, The University of Texas at El PasoFollow
Saeefa Rubaiyet Nowmi, The University of Texas at El PasoFollow
Ahmed Ann Noor Ryen, The University of Texas at El PasoFollow
Sabrina Saika, The University of Texas at El PasoFollow
Vladik Kreinovich, The University of Texas at El PasoFollow

Publication Date

4-1-2024

Comments

Technical Report: UTEP-CS-24-17

Abstract

In a computer, usually, all real numbers are stored by using the same number of bits: usually, 8 bytes, i.e., 64 bits. This amount of bits enables us to represent numbers with high accuracy -- up to 19 decimal digits. However, in most cases -- whether we process measurement results or whether we process expert-generated membership degrees -- we do not need that accuracy, so most bits are wasted. To save space, it is therefore reasonable to consider representations with varying number of bits. This would save space used for representing numbers themselves, but we would also need to store information about the length of each number. In view of this, the first natural question is whether a varying-length representation can lead to a drastic decrease in needed computer space. Another natural question is related to the fact that while potentially, allowing number of bits which is not proportional to 8 bits per byte will save even more space, this would require a drastic change in computer architecture, since the current architecture is based on bytes. So will going from bytes to bits be worth it -- will it save much space? In this paper, we provide answers to both questions.