Editing Binary-coded decimal (section)

==Comparison with pure binary==
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<!--as an alternative number system for computing and electronics imo a comparison to the standard one is justified (plugwash)-->

=== Advantages ===
* Scaling by a power of 10 is simple.
* [[Rounding]] at a decimal digit boundary is simpler. Addition and subtraction in decimal do not require rounding.{{dubious|Rounding|date=November 2021}}
* The alignment of two decimal numbers (for example 1.3 + 27.08) is a simple, exact shift.
* Conversion to a character form or for display (e.g., to a text-based format such as [[XML]], or to drive signals for a [[seven-segment display]]) is a simple per-digit mapping, and can be done in linear ([[Big-O notation|O]](''n'')) time. Conversion from pure [[binary number|binary]] involves relatively complex logic that spans digits, and for large numbers, no linear-time conversion algorithm is known (see {{section link|Binary number|Conversion to and from other numeral systems}}).
* Many non-integral values, such as decimal 0.2, have an infinite place-value representation in binary (.001100110011...) but have a finite place-value in binary-coded decimal (0.0010). Consequently, a system based on binary-coded decimal representations of decimal fractions avoids errors representing and calculating such values. This is useful in financial calculations.

=== Disadvantages ===
* Practical existing implementations of BCD are typically slower than operations on binary representations, especially on embedded systems, due to limited processor support for native BCD operations.<ref name="Mathur_1989" />
* Some operations are more complex to implement. [[Adder (electronics)|Adder]]s require extra logic to cause them to wrap and generate a carry early. Also, 15 to 20 per cent more circuitry is needed for BCD add compared to pure binary.{{Citation needed|date=May 2011}} Multiplication requires the use of algorithms that are somewhat more complex than shift-mask-add (a [[Binary numeral system#Multiplication|binary multiplication]], requiring binary shifts and adds or the equivalent, per-digit or group of digits is required).
* Standard BCD requires four bits per digit, roughly 20 per cent more space than a binary encoding (the ratio of 4 bits to log<sub>2</sub>10 bits is 1.204). When packed so that three digits are encoded in ten bits, the storage overhead is greatly reduced, at the expense of an encoding that is unaligned with the 8-bit byte boundaries common on existing hardware, resulting in slower implementations on these systems.<!-- Could add: encoding or decoding is trivial in software using a table lookup, and fast using direct logic otherwise. In hardware, it requires no more than three gate delays. -->