Representation of Integers

Joshi, Gandhar (2023). Representation of Integers. Postgraduate Research Poster Competition, The Open University.

Abstract

We describe or are taught to describe numbers in a particular manner we call the decimal number system. Computers understand the same using binary. In this study, we learn to define our own number system to represent integers (not necessarily with an integer geometric base) so that specific problems can be simplified when described in the newly defined number system. We use the Automata theory to explain the arithmetic relations (+,-,*,/) and equality relations (=,<,>) between the representations of integers and check the validity of their uniqueness. For example, the number 420 in decimal cannot be written in any other way using the same '0 to 9' digit set.

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