Aiken code

The Aiken code (also known as 2421 code)^[1][2] is a complementary binary-coded decimal (BCD) code. A group of four bits is assigned to the decimal digits from 0 to 9 according to the following table. The code was developed by Howard Hathaway Aiken and is still used today in digital clocks, pocket calculators and similar devices^{[citation needed]}.

Aiken code
Digits	4[1][2]
Tracks	4[1][2]
Digit values	2 4 2 1[1][2]
Weight(s)	0..4[1][2]
Continuity	no
Cyclic	no[1][2]
Minimum distance	1[1][2]
Maximum distance	4[1][2]
Redundancy	0.7
Lexicography	yes[1][2]
Complement	9[1][2]
v t e

The Aiken code differs from the standard 8421 BCD code in that the Aiken code does not weight the fourth digit as 8 as with the standard BCD code but with 2.

Aiken code (symmetry property)

Aiken code in hexadecimal coding

The following weighting is obtained for the Aiken code: 2-4-2-1.

One might think that double codes are possible for a number, for example 1011 and 0101 could represent 5. However, here one makes sure that the digits 0 to 4 are mirror image complementary to the numbers 5 to 9.

Aiken code
Decimal digit	Aiken 2 4 2 1 code[1][2]
0	0 0 0 0
1	0 0 0 1
2	0 0 1 0
3	0 0 1 1
4	0 1 0 0
5	1 0 1 1
6	1 1 0 0
7	1 1 0 1
8	1 1 1 0
9	1 1 1 1

See also

• Excess-3 code
• Gray code
• O'Brien code type I

References

1. Steinbuch, Karl W., ed. (1962). Taschenbuch der Nachrichtenverarbeitung [Handbook for Signal Processing] (in German) (1 ed.). Berlin / Göttingen / New York: Springer-Verlag OHG. pp. 71–74. LCCN 62-14511.
2. Steinbuch, Karl W.; Weber, Wolfgang; Heinemann, Traute, eds. (1974) [1967]. Struktur und Programmierung von EDV-Systemen [Handbook for Information Systems - Volume II - Structure and programming of computer systems]. Taschenbuch der Informatik – Band II (in German). Vol. II (3 ed.). Berlin, Germany: Springer Verlag. pp. 98–100. ISBN 3-540-06241-6. LCCN 73-80607.

Further reading

• White, Garland S. (October 1953). "Coded Decimal Number Systems for Digital Computers". Proceedings of the Institute of Radio Engineers. 41 (10). Institute of Radio Engineers (IRE): 1450–1452. doi:10.1109/JRPROC.1953.274330. eISSN 2162-6634. ISSN 0096-8390. S2CID 51674710. (3 pages)