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Suppose that I is the size of a T integer.
What is the maximum size of a string S that contains the digits of T arranged into characters?
For example:
T = 12345
S = '12345'
Actually, the basic equation only works for ASCII characters in ASCII or UTF-8 encoding; one byte per character. For UTF-16, these same characters would be encoded as 2 bytes each, and in UTF-32, 4 bytes each. This matters, depending on the programming language and runtime; .NET strings are stored and encoded in UTF-16.
So, it’s actually (log(N) + 1)*sizeof(char)