# What is a BCD Adder

A BCD Adder is a digital combinational circuit that is used for the addition of two numbers in BCD arithmetic’s.The primary difference between the binary and BCD arithmetic lays in the representation of the numbers greater than 9 in these two systems. The following truth table illustrates this difference:-

Decimal Number

Binary Representation

BCD Representation

10

1010

10000

11

1011

10001

12

1100

10010

13

1101

10011

14

1110

10100

15

1111

10101

16

10000

10110

17

10001

10111

18

10010

11000

19

10011

11001

Since 19 is the greatest possible sum in the addition of two 1-digit BCD numbers along with the carry bit from previous stage addition, only the table up to this number has been shown above.Now a BCD adder can be constructed by using a binary full adder circuit. But in case the output is greater than 9, the binary form has to be converted to its corresponding BCD form. This can be done by the use of additional logic circuitry.

If S0, S1, S2, S3, C3 are the output bits of the binary full adder where the bits have their usual meaning, then for output greater than 9, V becomes where V is:-

V = C1 + S3.S2 +S3.S1

When V is 1 i.e. the output becomes greater than 9, then the first four bits of the binary output from the full adder circuit can be converted in to its corresponding BCD representation by adding the number 0110. The fifth bit of the output which is always 1 for numbers greater than 9 can be represented by V.

We can also say that after synthesizing the logic of V, the sum bits from the first full adder circuit should be added to the number OVVO by using another full adder circuit. For numbers up to 9, V will remain 0 and 0000 will be added to the original sum bits and as a result render them as unchanged. For numbers greater than 9, 0110 will be added to the original sum bits and change them in to the corresponding BCD representation.

If B0, B1, B2, B3 are the output sum bits of the second full adder circuit, then the output is represented by BCD output VB3B2B1B0. In case of multi digit addition, BCD adders are used in cascade configuration. In this case, B3B2B1B0 will be the output of the stage while V will be the carry-in bit to the next stage of addition.