What are Half and Full Adders?

Full and half adders are the basic elements of digital logic used to perform addition operations in a binary system.

What is Half Adder?

Half Adder is a combinational logic circuit that is designed by connecting one XOR gate and one AND gate. The half-adder circuit has two inputs: A and B, which add two input digits and generate a carry and a sum.

Now, let's build a truth table for half adder.

What is Full Adder?

A Full Adder is an extension of the half adder that adds two single-bit binary numbers along with an additional Carry-in (Cin) from a previous stage. It produces:

1. Sum (S): The sum of the inputs and the carry-in.
2. Carry-out (Cout): The carry-out from the addition.

In simple terms, the Full Adder consists with 2 Half Adders and one logic gate OR.

Now, let's build the truth table for Full Adder values.

Conclusion:

1. Half Adder adds two bits.
2. Full Adder adds two bits and a carry-in, handling the carry distribution between bits in multi-bit addition.

Now, let's move on to Half and Full subtractor.

What is Half Subtractor?

A Half Subtractor is a digital circuit used to subtract two single-bit binary numbers. Like a half adder, it operates on two inputs, but instead of adding, it subtracts. The two outputs are:

1. Difference (D): Represents the difference between the two bits.
2. Borrow (B): Represents whether a "borrow" is required for the subtraction.

And again, build the truth table.

A half subtractor cannot handle the borrow from a previous stage, making it unsuitable for multi-bit subtraction.

What is Full Subtractor?

A Full Subtractor is an extension of the half subtractor. It subtracts two single-bit binary numbers along with an additional Borrow-in (Bin) from a previous stage. It produces:

1. Difference (D): The difference between the inputs and the borrow-in.
2. Borrow-out (Bout): The borrow generated if needed for further subtraction. The circuit diagram for a full subtractor usually consists of two half-subtractors and an additional OR gate to calculate the borrow-out bit.

And the truth table

Conclusion:

1. Half Subtractor: Subtracts two bits, gives the difference and a borrow.
2. Full Subtractor: Subtracts two bits with a borrow-in, handling multi-bit subtraction by distributing the borrow across stages.