The usual way of expressing a decimal number in terms of a binary number is known as pure binary coding and is discussed in the Number Systems section.

 A number of other techniques can be used to represent a decimal number. These are summarised below.

8421 BCD Code

In the 8421 Binary Coded Decimal (BCD) representation each decimal digit is converted to its 4-bit pure binary equivalent.

For example: 57_dec = 0101 0111_bcd

Addition is analogous to decimal addition with normal binary addition taking place from right to left. For example,

Where the result of any addition exceeds 9(1001) then six (0110) must be added to the sum to account for the six invalid BCD codes that are available with a 4-bit number.

This is illustrated in the example below

Note that in the last example the 1 that carried forward from the first group of 4 bits has made a new 4-bit number and so represents the "1" in "15".

In the examples above the BCD numbers are split at every 4-bit boundary to make reading them easier. This is not necessary when writing a BCD number down.

This coding is an example of a binary coded (each decimal number maps to four bits) weighted (each bit represents a number, 1, 2, 4, etc.) code.

4221 BCD Code

The 4221 BCD code is another binary coded decimal code where each bit is weighted by 4, 2, 2 and 1 respectively.

 Unlike BCD coding there are no invalid representations.

The decimal numbers 0 to 9 have the following 4221 equivalents

the 1's complement of a 4221 representation is important in decimal arithmetic. In forming the code remember the following rules

• Below decimal 5 use the right-most bit representing 2 first
• Above decimal 5 use the left-most bit representing 2 first
• Decimal 5 = 2+2+1 and not 4+1

Gray coding is a non-BCD, non-weighted reflected binary code.