Editing Scientific notation (section)

== Other bases <span class="anchor" id="B notation"></span><span class="anchor" id="H notation"></span><span class="anchor" id="O notation"></span><span class="anchor" id="C notation"></span><span class="anchor" id="P notation"></span> ==
While base ten is normally used for scientific notation, powers of other bases can be used too,<ref name="TI_1974_SR-22"/> base 2 being the next most commonly used one.

For example, in base-2 scientific notation, the number 1001<sub>b</sub> in [[binary numeral system|binary]] (=9<sub>d</sub>) is written as {{nowrap|1.001<sub>b</sub> × 2<sub>d</sub><sup>11<sub>b</sub></sup>}} or {{nowrap|1.001<sub>b</sub> × 10<sub>b</sub><sup>11<sub>b</sub></sup>}} using binary numbers (or shorter {{nowrap|1.001 × 10<sup>11</sup>}} if binary context is obvious).{{citation needed|date=March 2024}} In E notation, this is written as {{nowrap|1.001<sub>b</sub>E11<sub>b</sub>}} (or shorter: 1.001E11) with the letter "E" now standing for "times two (10<sub>b</sub>) to the power" here. In order to better distinguish this base-2 exponent from a base-10 exponent, a base-2 exponent is sometimes also indicated by using the letter "B" instead of "E",<ref name="HP16C-Lib"/> a shorthand notation originally proposed by [[Bruce Alan Martin]] of [[Brookhaven National Laboratory]] in 1968,<ref name="Martin_1968"/> as in {{nowrap|1.001<sub>b</sub>B11<sub>b</sub>}} (or shorter: 1.001B11). For comparison, the same number in [[decimal representation]]: {{nowrap|1.125 × 2<sup>3</sup>}} (using decimal representation), or 1.125B3 (still using decimal representation). Some calculators use a mixed representation for binary floating point numbers, where the exponent is displayed as decimal number even in binary mode, so the above becomes {{nowrap|1.001<sub>b</sub> × 10<sub>b</sub><sup>3<sub>d</sub></sup>}} or shorter 1.001B3.<ref name="HP16C-Lib"/>

This is closely related to the base-2 [[floating-point]] representation commonly used in computer arithmetic, and the usage of IEC [[binary prefixes]] (e.g. 1B10 for 1×2<sup>10</sup> ([[kibi-|kibi]]), 1B20 for 1×2<sup>20</sup> ([[mebi-|mebi]]), 1B30 for 1×2<sup>30</sup> ([[gibi-|gibi]]), 1B40 for 1×2<sup>40</sup> ([[tebi-|tebi]])).

Similar to "B" (or "b"<ref name="HP16C-Add"/>), the letters "H"<ref name="HP16C-Lib"/> (or "h"<ref name="HP16C-Add"/>) and "O"<ref name="HP16C-Lib"/> (or "o",<ref name="HP16C-Add"/> or "C"<ref name="HP16C-Lib"/>) are sometimes also used to indicate ''times 16 or 8 to the power'' as in 1.25 = {{nowrap|1.40<sub>h</sub> × 10<sub>h</sub><sup>0<sub>h</sub></sup>}} = 1.40H0 = 1.40h0, or 98000 = {{nowrap|2.7732<sub>o</sub> × 10<sub>o</sub><sup>5<sub>o</sub></sup>}} = 2.7732o5 = 2.7732C5.<ref name="HP16C-Lib"/>

Another similar convention to denote base-2 exponents is using a letter "P" (or "p", for "power"). In this notation the significand is always meant to be hexadecimal, whereas the exponent is always meant to be decimal.<ref name="Rationale_2003_C"/> This notation can be produced by implementations of the ''[[printf]]'' family of functions following the [[C99]] specification and ([[Single Unix Specification]]) [[IEEE Std 1003.1]] [[POSIX]] standard, when using the ''%a'' or ''%A'' conversion specifiers.<ref name="Rationale_2003_C"/><ref name="printf_2013"/><ref name="Beebe_2017_Hex"/> Starting with [[C++11]], [[C++]] I/O functions could parse and print the P notation as well. Meanwhile, the notation has been fully adopted by the language standard since [[C++17]].<ref name="C++17"/> [[Apple Inc.|Apple]]'s [[Swift (programming language)|Swift]] supports it as well.<ref name="Swift_2017"/> It is also required by the [[IEEE 754-2008]] binary floating-point standard. Example: 1.3DEp42 represents {{nowrap|1.3DE<sub>h</sub> × 2<sup>42</sup>}}.

[[Engineering notation]] can be viewed as a base-1000 scientific notation.