BCD (Binary Coded Decimal) Number System

BCD or Binary Coded Decimal is that number system or code which has the binary numbers or digits to represent a decimal number.

The BCD codes can be classified as:

• Weighted BCD Codes

• Self - complementing BCD Codes

• Cyclic Codes/ Gray Codes/ Reflected Codes

A decimal number contains 10 digits (0-9). Now the equivalent binary numbers can be found out of these 10 decimal numbers. In case of BCD the binary number formed by four binary digits, will be the equivalent code for the given decimal digits. In BCD we can use the binary number from 0000-1001 only, which are the decimal equivalent from 0-9 respectively. Suppose if a number have single decimal digit then it’s equivalent Binary Coded Decimal will be the respective four binary digits of that decimal number and if the number contains two decimal digits then it’s equivalent BCD will be the respective eight binary of the given decimal number. Four for the first decimal digit and next four for the second decimal digit. It may be cleared from an example.

Let, (12)₁₀ be the decimal number whose equivalent Binary coded decimal will be 00010010. Four bits from L.S.B is binary equivalent of 2 and next four is the binary equivalent of 1.

Table given below shows the binary and BCD codes for the decimal numbers 0 to 15.

From the table below, we can conclude that after 9 the decimal equivalent binary number is of four bit but in case of BCD it is an eight bit number. This is the main difference between Binary number and binary coded decimal. For 0 to 9 decimal numbers both binary and BCD is equal but when decimal number is more than one bit BCD differs from binary.

Decimal Digit	BCD 8 4 2 1
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	0 1 0 1
6	0 1 1 0
7	0 1 1 1
8	1 0 0 0
9	1 0 0 1