Let us consider a common way to represent non-negative integers. An integer will be represented in radix using the notation
We will call an -digit number and its digits. Zero will be represented with no digits, . Observe that
for any .
Unless stated otherwise we will always have that the most-significant digit is non-zero, that is, for . This assumption has some important consequences. First, that
for any . Secondly, that each non-negative integer has a unique representation, that is, to each number and radix corresponds exactly one and digits such that . Thirdly, that
This last relation can be quite useful since the number of needed digits can be found, given and . For instance, the fact that means that the number 1317803400 can be represented using 31 binary digits.
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