BCD (Binary Coded Decimal) Number System

You should now be familiar with the Binary, Decimal and Hexadecimal Number System. If we view single digit values for hex, the numbers 0 - F, they represent the values 0 - 15 in decimal, and occupy a nibble. Often, we wish to use a binary equivalent of the decimal system. This system is called Binary Coded Decimal or BCD which also occupies a nibble. In BCD, the binary patterns 1010 through 1111 do not represent valid BCD numbers, and cannot be used.

Conversion from Decimal to BCD is straightforward. You merely assign each digit of the decimal number to a byte and convert 0 through 9 to 00000000 through 00001001, but you cannot perform the repeated division by 2 as you did to convert decimal to binary.

Let us see how this works. Determine the BCD value for the decimal number 5,319. Since there are four digits in our decimal number, there are four bytes in our BCD number. They are:

Since computer storage requires the minimum of 1 byte, you can see that the upper nibble of each BCD number is wasted storage. BCD is still a weighted position number system so you may perform mathematics, but we must use special techniques in order to obtain a correct answer.