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A BCD adder is a digital circuit
to add two BCD numbers and produces the sum as a BCD number. When a BCD number is
added to another BCD number using a 4-bit binary full adder, following 3 cases
may arise:
1. Sum
is less than or equal to 9 with carry 0.
2. Sum
is greater than 9 with carry 0.
3. Sum
is less than or equal to 9 with carry 1.
In the first case the sum is a valid
BCD number and no further process is needed, but in the second and third cases
the sum is not valid and should be converted into BCD numbers. To make such a
correction a factor of 6 (in binary) is added to the sum to obtain the final
result.
The logic expression to check if
the sum of two 4-bit binary numbers A3A2A1A0
and B3B2B1B0 => S3S2S1S0
exceeds 9 is given by,
Y = S3S2 + S3S1
With these points, a BCD adder
circuit can be designed as shown in the following diagram.
As shown in the figure, the two
BCD numbers, together with input carry, are first added in the top 4-bit binary
adder to produce a binary sum. When the output carry is equal to zero
(i.e. when sum ≤ 9 and Cout = 0) nothing (zero) is added to the
binary sum. When it is equal to one (i.e. when sum > 9 or Cout
= 1), binary 0110 is added to the binary sum through the bottom 4-bit binary
adder. The output carry generated from the bottom binary adder is ignored
as it is already available at the output carry terminal.