The digital systems handles the decimal number in the form of binary coded decimal numbers (BCD). A BCD Adder Circuit that adds two BCD digits and produces a sum digit also in BCD. BCD numbers use 10 digits, 0 to 9 which are represented in the binary form 0 0 0 0 to 1 0 0 1, i.e. each BCD digit is represented as a 4-bit binary number. When we write BCD number say 526, it can be represented as

Here, we should note that BCD cannot be greater than 9.

The addition of two BCD numbers can be best understood by considering the three cases that occur when two BCD digits are added.

#### Sum Equals 9 or less with carry 0

Let us consider additions of 3 and 6 in BCD.

The addition is carried out as in normal binary addition and the sum is 1 0 0 1, which is BCD code for 9.

#### Sum greater than 9 with carry 0

Let us consider addition of 6 and 8 in BCD

The sum 1 1 1 0 is an invalid BCD number. This has occurred because the sum of the two digits exceeds 9. Whenever this occurs the sum has to be corrected by the addition of six (0110) in the invalid BCD number, as shown below

After addition of 6 carry is produced into the second decimal position.

#### Sum equals 9 or less with carry 1

Let us consider addition of 8 and 9 in BCD

In this, case, result (0001 0001) is valid BCD number, but it is incorrect. To get the correct BCD result correction factor of 6 has to be added to the least significant digit sum, as shown below

Going through these three cases of BCD addition we can summarise the BCD addition procedure as follows :

2. If four-bit sum is equal to or less than 9, no correction is needed. The sum is in proper BCD form.
3. If the four-bit sum is greater than 9 or if a carry is generated from the four-bit sum, the sum is invalid.
4. To correct the invalid sum, add 01102 to the four-bit sum. If a carry results from this addition, add it to the next higher-order BCD digit.

Thus to implement BCD Adder Circuit we require :