BINARY CODED DECIMAL (BCD)

DEFINITION: The word BINARY CODED DECIMAL stands for Decimal number 0 - 9 in which four bits binary number 0000 to 1001 are used to represent each digit of the the decimal numeral. Or can be seen as decimal numbers coded with four bits binary numbers.

In BCD each number is defined by a binary code of 4 bits. The Code is           8 - 4 - 2 - 1, it indicate the weights of each bit 2³ – 2² – 2¹ - 2⁰  
Any number that is beyond 9 will be considered to have 2 digits and each digit will have its four bits binary equivalent. That is, for example, 12 will have its binary equivalent for 1 and 2, which is 0001 0010. 
E.g. 542 = 0101  0100  0010.
                   5       4        2

The difference between the ordinary four bit binary number and BCD is that binary number of decimal numbers greater than 9  is still four bits which ends with 1111 representing 15, while in BCD, it is 8 bits.
the table below shows the decimal,binary and BCD equivalent.



CONVERSION FROM BINARY TO BCD

When Binary numbers are added and the result is not greater than 9, the equivalent binary number is always the same with the BCD. But when it is greater than 9, the binary value will not be valid in BCD. For example, if the result is 15, that is, 1111 it has to be converted to BCD. To do so, 6 (0110) has to be added to the result.
                                         15 =        1111
                                           6 =        0110
                                                        0101
From the addition, the leftmost addition has a carry of 1, which is carried to the next place value.
The result is 0001 0101 which correspond to what we have on the table.
To prove this, the difference between any BCD and corresponding Binary is 6 (0110).

Why number 6 added ? 6 is being added to binary numbers because after 9 there are 6 additional digits to complete the 4- bits binary number of 1111. So, to reset the excess binary number back to 9 (1001) or binary that is within the BCD range 6 (0110) is added to make the counting skip the remaining six decimal values i.e from 10 to 15 which does not obey BCD to return to the BCD codes.

USES OF BCD CODE

BCD Code find usefulness when processing numerical values to be transmitted and display by digital electronic devices which uses seven segment display devices. This device is found in Calculator, Digital Watches.

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