BCD Adder

N-bit parallel Adder

The Full Adder can only add two single digit binary number along with carry input. But practically we have to add binary numbers longer than just 1-bit. Hence, to add 2 n-bit binary numbers we have to use n-bit parallel adder. N-bit parallel adder uses several full adders. In it, the carry output of the previous full adder is connected to the next full adder as the carry input. 

Lets see a 4-bit parallel adder as an example.

4-bit parallel adder

The first adder in the 4-bit parallel adder is the lowest stage, hence Cᵢₙ is taken as 0. Further the circuit works in the same way,i.e., the carry output of first full adder goes as a carry input in second full adder and this continues.

The logic circuit for a 4-bit adder is given below:

Here, A₀ and B₀ are the LSB of the 4-bit numbers A and B.

N-bit parallel Subtractor

As we know, using 1's or 2's complement we can easily perform subtraction. Hence, we can use binary adder to perform binary subtraction. So, we can easily perform subtraction of two n-bit numbers using binary adder only.

Let us see a 4-bit parallel subtractor as an example.

4-bit parallel subtractor

The number to be subtracted is first inverted to get its 1's complement and after that 4-bit adder is used to add A and 2's Complement of B to produce the subtraction. The logic circuit of 4-bit parallel subtractor is given below.

 S3 S2 S1 S0 represents the result of binary subtraction (A-B) and carry output Cₒᵤₜ represents the polarity of the result. If A > B Cₒᵤₜ = 0 and the result of binary form (A-B) then Cₒᵤₜ = 1 and the result is in the 2’s complement form

BCD Addder

The steps for binary coded decimal addition are given below :

1. Add the BCD code groups for each decimal digit position using ordinary binary addition.

2. For those positions where the sum is 9 or less, the sum is in proper BCD form and no correction is needed to be made.

3. When the sum of two digits is greater than 9, a correction of 0110 (binary number for 6) should be added to that sum to produce the proper BCD result. This will produce a carry to be added to the next decimal position.

A BCD adder is a circuit that adds two BCD digits in parallel and produces a sum BCD digit and a carry out bit.

Thus to implement BCD Adder Circuit what we need is:

• 4-bit binary adder for initial addition
• Logic circuit to detect sum greater than 9 and
• One more 4-bit adder to add 0110 in the sum if sum is greater than 9 or carry is 1.

The logic circuit to detect sum greater than 9 can be determined by simplifying the boolean expression of given BCD Adder Truth Table:

If we detect the numbers 1010 to 1111 (10 to 15) through K-Map, we will get:

Y = S₃S₂ + S₃S₁

So, the logic circuit for the BCD Adder is given below:

The two BCD digits, together with the input carry, are first added in the top 4-bit binary adder to produce the binary sum. The bottom 4-bit binary adder is used to add the correction factor to the binary result of the top binary adder.