least significant digit

The least significant digit of a number $n$ written in a given positional base $b$ is the digit in the least significant place value, and has to be in the range $-1<d_{1}<b$ . In the case of an integer, the least significant digit is the 1’s place value, usually written to the right of the $b$ ’s place value. In the case of a transcendental number, there is no actual least significant digit, but for computational purposes the rational approximation would have a least significant digit.

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 $d_{i}b^{i}$ rather than $d_{i}b^{k-i}$ .) For an array of digits meant for text string manipulation, however, the least significant digit might be placed at position $k$ (for example, by Mathematica’s IntegerDigits function).

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

单词	LeastSignificantDigit
释义	least significant digit The least significant digit of a number $n$ written in a given positional base $b$ is the digit in the least significant place value, and has to be in the range $-1<d_{1}<b$ . In the case of an integer, the least significant digit is the 1’s place value, usually written to the right of the $b$ ’s place value. In the case of a transcendental number, there is no actual least significant digit, but for computational purposes the rational approximation would have a least significant digit. 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 $d_{i}b^{i}$ rather than $d_{i}b^{k-i}$ .) For an array of digits meant for text string manipulation, however, the least significant digit might be placed at position $k$ (for example, by Mathematica’s IntegerDigits function). In binary, the least significant digit is often called the least significant bit.
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