Number Representation

Abstract

We are accustomed to using the decimal number system. For example the (decimal) number 34062 can be written as

$$34062 = 3\cdot {10^4} + 4\cdot {10^3} + 0\cdot {10^2} + 6\cdot {10^1} + 2\cdot {10^0}$$

where 10¹ = 10 and 10⁰ = 1. In general, any positive integer can be represented in one and only one way in the form

$${a_0}\cdot {10^0} + {a_1}\cdot {10^1} + {a_2}\cdot {10^2} + \ldots + {a_k}\cdot {10^k}$$

where 0 < a _i < 9 for 0 < i < k and a _k > 0. This number is denoted

$${a_k}{a_{k - 1}} \ldots {a_2}{a_1}{a_0}$$

in standard decimal notation.