In this lecture, we are going to learn about the what is BCD adder, the BCD adder circuit diagram, the BCD adder truth table, the BCD adder block diagram, and the operation of the BCD Adder in every detail.

Computers to calculators that carry out the arithmetic operations directly in the decimal number system represent the decimal numbers in the BCD form. In this lecture, we will discuss the BCD Adder in detail and then in the next lecture, we will cover the BCD subtractor circuit.

## What is BCD Adder

- A BCD Adder adds two BCD digits and produces a BCD digit, A BCD cannot be greater than 9.

- The two given BCD numbers are to be added using the rules of binary addition.

- If the sum is less than or equal to 9 and carry = 0, then no correction is necessary. The sum is correct and in the true BCD form.

- But if the sum is invalid BCD or carry = 1, then the result is wrong and needs correction.

- The wrong result can be corrected by adding six (0110) to it.

## BCD Adder Block Diagram

From the above point which we have discussed, we understand that the 4 bit BCD adder should consist of the following blocks.

- A 4 bit binary adder to add the given numbers A and B.
- A combinational circuit to check if the sum is greater than 9 or carry = 1.
- One or more 4-bit binary adder to add six (0110) to the incorrect sum if sum > 9 or carry 1.

The block diagram of such a BCD adder is shown in the figure below.

From the above discussed, we can conclude that before getting the knowledge about eh operation of BCD adder, we have to design a combinational circuit that sense if the sum is greater than 9 or carry=1.

## Design of Combination circuit of BCD adder

To design any combinational circuit, we have to make a truth table for that combinational circuit, and by using the k-map we have to realize the expression for that logic diagram to build the circuit.

Here, the output of the combinational circuit should be 1 if the sum produced by the adder is greater than 9 i.e. 1001. The truth table is as follows:

### BCD Adder Truth Table

From the truth table, we can see that, when the sum is valid BCD numbers then Y = 0, and when the sum is invalid BCD numbers then Y = 1.

So from the above truth table now we are going to make the combinational circuit for the BCD adder so correct the BCD number when the invalid BCD number is getting from the output.

To build the combination circuit now we will use k-map to realize the boolean expression for the combinational circuit.

### K-Map for BCD adder combination circuit

The K-map for output Y of the combination circuit of the BCD adder is shown in the figure below:

From the above K-map, we can write the Boolean expression as:

\mathbf{Y = S_3S_2 + S_3S_1}

Also Read:Magnitude Comparator and Digital Comparator

## BCD Adder Circuit Diagram

The BCD adder circuit is shown in the below figure.

We can make a BCD adder using ic 7483 as per the below image.

The output of the combinational circuit should be 1 if the Cout of adder-1 is high. therefore Y is ORed with Cout of the adder 1 as shown in the figure.

the output of the combinational circuit is connected to B_{1}B_{2} inputs of adder-2 and B_{3}=B_{1}=0 as they are connected to the ground permanently. This makes B_{3}B_{2}B_{1}B_{0} = 0 1 1 0 if Y’ = 1.

The sum outputs of adder-1 are applied to A_{3}A_{2}A_{1}A_{0} of adder-2. The output of the combinational circuit is to be used as the final output carry and the carry output of adder-2 is to be ignored.

## Operation of BCD Adder

So now we are going to see the actual operation of BCD adder and how bcd adder works. For reference please check the above figure while studying the operation of the BCD adder.

### Case 1: Sum <= 9 and Carry = 0

- The output of combinational circuit Y’ = 0. Hence B
_{3}B_{2}B_{1}B_{0}= 0000 for adder-2. - Hence the output of adder-2 is the same as that of adder-2.

### Case 2: Sum > 9 and Carry = 0

- If S
_{3}S_{2}S_{1}S_{0}of adder-1 is greater than 9, then output Y’ of the combinational circuit becomes 1. - Therefore B
_{3}B_{2}B_{1}B_{0}= 0110 (adder-2). - hence six(0110) will be added to the sum output of adder-1.
- We get the corrected BCD result at the output of adder-2

### Case 3: Sum <= 9 and Carry = 1

- As the carry output of adder-1 is high, Y’ = 1.
- Therefore B
_{3}B_{2}B_{1}B_{0}= 0110 (adder-2) - So, 0110 will be added to the sum output of adder-1.
- We get the corrected BCD result at the output of adder-2.

Thus, we can make a 4-bit BCD adder using the binary adder.

Also Read:Half Adder in Digital Electronics

## 8-bit BCD adder using IC 7483

The 8-bit BCD adder using the 4-bit BCD adder using 7483 is shown in the figure below.

We have to use two 4-bit adders. the carry-out of the lower 4-bit adder is applied to carry input of the next 4-bit adder.

The concept of adding 6 (0110) for correction purposes is used in this circuit as well.

You can learn the IC 7483 datasheet from the below link:

IC 7483 Datasheet | Click here |

Also Read:4 Bit Binary To BCD Converter