Implementation of Full Adder using Half Adders and OR gates

A full adder is a combinational circuit that can add three bits together and produce a sum and a carry bit. It is commonly used in arithmetic circuits and is an important building block for many digital systems.

A half adder is a combinational logic circuit that can add two one-bit inputs and produce a sum and a carry output. It can be implemented using a XOR gate and an AND gate.

To implement a full adder using half adders and OR gates, we need to combine two half adders and use an OR gate to produce the final carry output. Here's how it works:

1. Implementing a Half Adder

A half adder can be implemented using a XOR gate and an AND gate as shown below:


The truth table for the half adder is as follows:

| Input A | Input B | Sum | Carry |
|---------|---------|-----|-------|
| 0 | 0 | 0 | 0 |
| 0 | 1 | 1 | 0 |
| 1 | 0 | 1 | 0 |
| 1 | 1 | 0 | 1 |

2. Implementing a Full Adder using Half Adders and OR gates

To implement a full adder using half adders and OR gates, we need to combine two half adders and use an OR gate to produce the final carry output. Here's how it works:

- We first use two half adders to add the least significant bits (LSBs) of the two numbers to be added. The sum output from the first half adder is the LSB of the final sum, and the carry output from the first half adder is the carry input to the second half adder.
- We then use another half adder to add the next least significant bits (the second bits) of the two numbers and the carry output from the first half adder. The sum output from this half adder is the second bit of the final sum, and the carry output from this half adder is the carry input to the next stage.
- We continue this process for all four bits of the two input numbers.

At the end, we have four sum bits and a final carry bit. The four sum bits are combined to produce the final sum using a 4-input OR gate.

Here's the circuit diagram for a 4-bit parallel adder implemented using half adders and OR gates:


As you can see, we need a total of 7 half adders and 3 OR gates to implement a 4-bit parallel adder using half adders and OR gates.

Hence, the correct answer is option 'C' (7 half adders and 3 OR gates).