# Half Subtracter Using NAND Gates

<Back

## Aim

To study and verify the Half Subtracter using NAND Gates.

## Learning Objectives

1. To understand the behavior and demonstrate Half Subtracter Using NAND Gates.
2. To apply knowledge of the fundamental gates to create truth tables.
3. To develop digital circuit building and troubleshooting skills.
4. To understand key elements of TTL logic specification or datasheets.

## IC Used

For Half Subtracter Using NAND Gates:
IC NumberIC Name

## Procedure

1. Place the IC on IC Trainer Kit.
2. Connect VCC and ground to respective pins of IC Trainer Kit.
3. Implement the circuit as shown in the circuit diagram.
4. Connect the inputs to the input switches provided in the IC Trainer Kit.
5. Connect the outputs to the switches of O/P LEDs
6. Apply various combinations of inputs according to the truth table and observe the condition of LEDs.
7. Note down the corresponding output readings for various combinations of inputs.
8. Power Off Trainer Kit, disconnect all the wire connections and remove IC's from IC-Base.

## Theory

HALF SUBTRACTER - ​​ The circuit, which performs the subtraction of two binary numbers is known as Binary subtractor. Half subtractor is the most essential combinational logic circuit which is used in digital electronics. Basically, this is an electronic device or in other terms, we can say it as a logic circuit. Half subtractor is used to perform two binary digits subtraction.

In half subtraction, the process of subtraction is similar to arithmetic subtraction. In arithmetic subtraction the base 2 number system is used whereas in binary subtraction, binary numbers are used for subtraction. The resultant terms can be denoted with the difference and borrow.

As in binary subtraction, the major digit is 1, we can generate borrow while the subtrahend 1 is superior to minuend 0 and due to this, borrow will need.

NAND gate - It is a digital circuit that has two or more inputs and produces an output, which is the inversion of logical AND of all those inputs.

Logic NAND Gates are available using digital circuits to produce the desired logical function and is given a symbol whose shape is that of a standard AND gate with a circle, sometimes called an "inversion bubble" at its output to represent the NOT gate symbol with the logical operation of the NAND gate.

As with the AND function seen previously, the NAND function can also have any number of individual inputs and commercial available NAND Gate IC's are available in standard 2, 3, or 4 input types. If additional inputs are required, then the standard NAND gates can be cascaded together to provide more inputs.

Boolean Expression Y = (A.B)'

"If either A or B are NOT true, then Y is true"

NAND gate operation is same as that of AND gate followed by an inverter. That's why the NAND gate symbol is represented like that.

## Precautions

1. Make the connections according to the IC pin diagram.
2. The connections should be tight on trainer kit.
3. The Vcc and ground should be applied carefully at the specified pin only.

## Conclusion

We have learned the Half Subtracter Using NAND Gates.