Editing Binary-coded decimal (section)

==Alternative encodings==
If errors in representation and computation are more important than the speed of conversion to and from display, a scaled binary representation may be used, which stores a decimal number as a binary-encoded integer and a binary-encoded signed decimal exponent. For example, 0.2 can be represented as 2{{e|-1}}.

This representation allows rapid multiplication and division, but may require shifting by a power of 10 during addition and subtraction to align the decimal points. It is appropriate for applications with a fixed number of decimal places that do not then require this adjustment—particularly financial applications where 2 or 4 digits after the decimal point are usually enough. Indeed, this is almost a form of [[fixed point arithmetic]] since the position of the [[radix point]] is implied.

The [[Hertz encoding|Hertz]] and [[Chen–Ho encoding]]s provide Boolean transformations for converting groups of three BCD-encoded digits to and from 10-bit values<ref group="nb" name="Pseudo-tetrades"/> that can be efficiently encoded in hardware with only 2 or 3 gate delays. [[Densely packed decimal]] (DPD) is a similar scheme<ref group="nb" name="Pseudo-tetrades"/> that is used for most of the [[significand]], except the lead digit, for one of the two alternative decimal encodings specified in the [[IEEE 754-2008]] floating-point standard.