Aiken code

From HandWiki
Short description: Complementary binary-coded decimal code
Aiken code
Digits4[1][2]
Tracks4[1][2]
Digit values2 4 2 1[1][2]
Weight(s)0..4[1][2]
Continuityno
Cyclicno[1][2]
Minimum distance1[1][2]
Maximum distance4[1][2]
Redundancy0.7
Lexicographyyes[1][2]
Complement9[1][2]

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].

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

References

  1. 1.00 1.01 1.02 1.03 1.04 1.05 1.06 1.07 1.08 1.09 1.10 (in German) Taschenbuch der Nachrichtenverarbeitung (1 ed.). Berlin / Göttingen / New York: Springer-Verlag OHG. 1962. pp. 71–74. 
  2. 2.00 2.01 2.02 2.03 2.04 2.05 2.06 2.07 2.08 2.09 2.10 (in German) Struktur und Programmierung von EDV-Systemen. Taschenbuch der Informatik – Band II. II (3 ed.). Berlin, Germany: Springer Verlag. 1974. pp. 98–100. ISBN 3-540-06241-6. 

Further reading