Binary-coded decimal: Difference between revisions

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=== 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 log₂10 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. -->

==Representational variations==

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<ref name="Glixon_1957">{{cite journal |date=March 1957 |title=Can You Take Advantage of the Cyclic Binary-Decimal Code? |author-first=Harry Robert |author-last=Glixon |journal=[[Control Engineering (magazine)|Control Engineering]] |issn=0010-8049 |publisher=[[Technical Publishing Company]], a division of Dun-Donnelley Publishing Corporation, [[Dun & Bradstreet Corp.]] |volume=4 |number=3 |pages=<!-- 3, -->87–91 |url=https://books.google.com/books?id=-_5IAQAAIAAJ}}<!-- https://web.archive.org/web/20180115014809/https://donmooreswartales.com/2010/05/12/harry-glixon/ https://books.google.com/books?id=-_5IAQAAIAAJ&focus=searchwithinvolume&q=cyclic+binary+code --> (5 pages)</ref>

<ref name="White_1953">{{cite journal |title=Coded Decimal Number Systems for Digital Computers |author-first=Garland S. |author-last=White |journal=[[Proceedings of the Institute of Radio Engineers]] |publisher=[[Institute of Radio Engineers]] (IRE) |issn=0096-8390 |eissn=2162-6634 |volume=41 |number=10 |date=October 1953 |doi=10.1109/JRPROC.1953.274330 |s2cid=51674710 |pages=1450–1452}} (3 pages)</ref>

<ref name="Lucal_1959">{{cite journal |author-first=Harold M. |author-last=Lucal |title=Arithmetic Operations for Digital Computers Using a Modified Reflected Binary |journal=[[IRE Transactions on Electronic Computers]] |volume=EC-8 |number=4 |pages=449–458 |date=December 1959 |issn=0367-9950 |doi=10.1109/TEC.1959.5222057 |s2cid=206673385 |url=https://ieeexplore.ieee.org/document/5222057|url-access=subscription }} (10 pages)</ref>

<ref name="EHub_2015">{{cite web |title=Different Types of Binary Codes |at=Section 2.4 5211 Code |date=2019-05-01 |orig-date=2015-01-28 |work=Electronic Hub |url=https://www.electronicshub.org/disclaimer/ |access-date=2020-08-04 |url-status=live |archive-url=https://web.archive.org/web/20200518203953/https://www.electronicshub.org/disclaimer/ |archive-date=2020-05-18}}</ref>

<ref name="Paul_1995">{{cite web |author-first=Matthias R. |author-last=Paul |title=Unterbrechungsfreier Schleifencode |language=de |trans-title=Continuous loop code |version=1.02 |url=http://www.uni-bonn.de/~uzs180/download/mpbcd102.zip |date=1995-08-10 |orig-date=1994 |access-date=2008-02-11}}{{cbignore}} (NB. The author called this code {{lang|de|Schleifencode}} (English: "loop code"). It differs from [[Gray BCD code]] only in the encoding of state 0 to make it a cyclic [[unit-distance code]] for full-circle rotatory [[slip ring]] applications. Avoiding the all-zero code pattern allows for loop self-testing and to use the data lines for uninterrupted power distribution.)</ref>