It is necessary to explain some terms for the correct understanding of this section. The pure binary code is based on a rule (power of two), whilst the BCD codes are based on a table where the decimal numbers from 0 to 9 are shown and their corresponding "translations" in BCD. There are several types of BCD:

• Pure BCD: Binary Code Digit, it is a standard to represent decimal numbers in binary system, where each decimal digit is coded as a sequence of 4 bits.
• BCDS XS3: the conversion is done adding 3 units to the decimal number that we want to transform into a binary number.
• Aiken: code similar to natural BCD where the "weights" or "values" are distributed in a different manner. In the natural BCD, the weights are: 8-4-2-1, in the Aiken code, the distribution is: 2-4-2-1.

If the previous codes are based on a rule, these are based on a table. The method consists on replacing each digital number by the 4 corresponding bits.

Decimal	BCD puro	BCD XS3	Aiken	BCD 5421
0	0000	0011	0000	0000
1	0001	0100	0001	0001
2	0010	0101	0010	0010
3	0011	0110	0011	0011
4	0100	0111	0100	0100
5	0101	1000	1011	1000
6	0110	1001	1100	1001
7	0111	1010	1101	1010
8	1000	1011	1110	1011
9	1001	1100	1111	1100

Thus, in BCD 13 is written as 1 (0001) followed by 3 (0011): 13 in decimal is written as 00010011 in BCD. The same number in XS3 is written as 01000110.

To pass from decimal to binary, and vice versa, you simply need the conversion table (dictionary) in front of you, or to know it by hard. The BCD table is very simple.