PlanetMath (more info)
 Math for the people, by the people.
Encyclopedia | Requests | Forums | Docs | Wiki | Random | RSS  
Login
create new user
name:
pass:
forget your password?
Main Menu
Owner confidence rating: High Entry average rating: No information on entry rating
least significant digit (Definition)

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_ib^i$ rather than $ d_ib^{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.



"least significant digit" is owned by PrimeFan. [ owner history (1) ]
(view preamble | get metadata)

View style:

Also defines:  least significant bit
Log in to rate this entry.
(view current ratings)

Cross-references: binary, function, Mathematica's, string, index, approximation, rational, transcendental number, right, integer, range, place, digit, base, number
There are 28 references to this entry.

This is version 2 of least significant digit, born on 2006-10-27, modified 2006-10-31.
Object id is 8486, canonical name is LeastSignificantDigit.
Accessed 2342 times total.

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

Pending Errata and Addenda
None.
[ View all 1 ]
Discussion
Style: Expand: Order:
forum policy

No messages.

Interact
post | correct | update request | add derivation | add example | add (any)