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Now let us see the arithmetic addition of two decimal digits in the BCD, with a possible carry from previous stage. As each input digit does not exceed 9, output sum cannot be greater than 9 + 9 + 1 = 19, this1 in the sum being an input-carry. Assume we apply two BCD digits to a 4-bit binary adder. The adder will form sum in binary and produce a result which may range from 0 to 19. The output sum of the two decimal numbers must be represented in BCD and should appear in form listed in second column of table. The problem is to find a simple rule by which binary column of table. The problem is to find out a simple rule so that binary number in first column can be converted to correct BCD digit representation of number in the second column.

It is apparent that when binary sum is equal to or less than 1001, no change is needed. When binary sum is greater than 1001, we have to to add of binary 6 (0110) to binary sum to find correct BCD representation and to produces output-carry as required.

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