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most significant digit (Definition)

The most significant digit of a number $ n$ written in a given positional base $ b$ is the digit in the most significant place value, and has to be in the range $ -1 < d_k < b$. In the case of an integer, the most significant digit is the $ b^k$'s place value, where $ k$ is the total number of digits, or $ k = \lfloor log_{b} n \rfloor$.

In an array of digits $ k$ long meant for mathematical manipulation, it might be convenient to index the least significant digit with index 1 or 0, and the more significant digits with larger integers. (This enables the calculation of the value of a given digit as $ d_ib^i$ rather than $ d_ib^{k - i}$.) For an array of digits meant for text string manipulation, however, the most significant digit might be placed at position 0 or 1 (for example, by Mathematica's IntegerDigits function).

In binary, the most significant digit is often called the most significant bit.



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Cross-references: binary, function, Mathematica's, string, least significant digit, index, integer, range, place, digit, base, number
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This is version 1 of most significant digit, born on 2007-03-27.
Object id is 9122, canonical name is MostSignificantDigit.
Accessed 457 times total.

Classification:
AMS MSC11A63 (Number theory :: Elementary number theory :: Radix representation; digital problems)

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