Design BDC adder.

A BCD (Binary Coded Decimal) adder is a circuit that adds two BCD digits in parallel and produces a result which is also a BCD. The BCD adder is a digital circuit that performs binary addition. It is also called a 4-bit binary adder.

The BCD adder is designed using the 4-bit binary adder and an OR gate. The 4-bit binary adder is used to add the two BCD numbers, and the OR gate is used to check for the condition of the sum greater than 9.

Let's design a BCD adder:

Step 1: First, we need to design a 4-bit binary adder. A 4-bit binary adder is a circuit that adds two 4-bit binary numbers and produces a 4-bit binary sum and a carry. The 4-bit binary adder can be designed using four 1-bit full adders. The first full adder takes the least significant bits and the carry in is set to 0. The carry out of the first full adder is connected to the carry in of the second full adder, and so on.

Step 2: Next, we need to design a circuit that checks if the 4-bit binary sum is greater than 9. This can be done using an OR gate. The OR gate takes the most significant bit and the carry out of the 4-bit binary adder as inputs and produces an output that is 1 if either of the inputs is 1.

Step 3: The output of the OR gate is connected to the carry in of the 4-bit binary adder. If the 4-bit binary sum is greater than 9, the carry in is set to 1 and the 4-bit binary sum is incremented by 1.

Step 4: The 4-bit binary sum and the carry out of the 4-bit binary adder are the outputs of the BCD adder.

Here is the truth table for the BCD adder:

A	B	Sum	Carry
0	0	0	0
0	1	1	0
1	0	1	0
1	1	0	1

In the table, A and B are the inputs, Sum is the output of the 4-bit binary adder, and Carry is the output of the OR gate.

For example, if A = 0101 (5 in decimal) and B = 0100 (4 in decimal), the 4-bit binary adder produces a sum of 1001 (9 in decimal) and a carry of 0. The OR gate produces an output of 0 because the sum is not greater than 9. Therefore, the BCD adder produces a sum of 1001 and a carry of 0.

In conclusion, a BCD adder is a digital circuit that adds two BCD digits and produces a BCD sum. It is designed using a 4-bit binary adder and an OR gate. The 4-bit binary adder adds the two BCD digits, and the OR gate checks for the condition of the sum greater than 9. The sum and the carry are the outputs of the BCD adder.