## Aiken code

It is recommended to read the tutorial on the **Binary number system** before you start reading this tutorial. Aiken BCD code is similar to the natural BCD code, but with “weights” or “values” distributed differently. On the natural BCD, weights are: 8 – 4 – 2 – 1. On the **Aiken code**, the distribution is: 2 – 4 – 2 – 1.

The reason for this coding is to achieve symmetry between certain numbers. View the symmetry in the corresponding Aiken codes for decimal numbers: 4 and 5, 3 and 6, 2 and 7, 1 and 8, 0 and 9.

## Decimal to Aiken Conversion table

Each number is the 9 complement of its symmetrical number, for all digits. The “1” becomes “0” and “0” becomes “1”. For example: 3 (0011) and 6 (1100). We must take into account the new “weights” on this code. The **Aiken code** is useful for operations of subtraction and division.

You may be interested on: **The Gray Code, truth table and applications**

## Excess 3 Code

The Excess 3 Code is obtained by adding “3” to each combination of the natural BCD code.

The Excess 3 code is a code where the weighting does not exist (no “weights” as in the natural BCD and Aiken code).

Like the Aiken code, the **Excess 3 code **meets the same characteristic of symmetry. Each number is the 9 complement of its symmetrical number, for all digits.

## Decimal to BCD to Excess 3 Conversion table

See the Excess 3 code symmetry, which corresponds to the decimal numbers: 4 and 5, 3 and 6, 2 and 7, 1 and 8, 0 and 9. It is a useful code in the operations of subtraction and division.