- Trending Categories
- Data Structure
- Networking
- RDBMS
- Operating System
- Java
- MS Excel
- iOS
- HTML
- CSS
- Android
- Python
- C Programming
- C++
- C#
- MongoDB
- MySQL
- Javascript
- PHP
- Physics
- Chemistry
- Biology
- Mathematics
- English
- Economics
- Psychology
- Social Studies
- Fashion Studies
- Legal Studies

- Selected Reading
- UPSC IAS Exams Notes
- Developer's Best Practices
- Questions and Answers
- Effective Resume Writing
- HR Interview Questions
- Computer Glossary
- Who is Who

# Realization of a Full Subtractor using Two Half Subtractors

A subtractor is a combinational logic circuit that can perform the subtraction of two numbers (or binary numbers) and produce the difference between them. It is a combinational logic circuit. Therefore, the output of the subtractor depends only on its present inputs.

There are two types of subtractors namely,

Half Subtractor

Full Subtractor

Read this tutorial to find out how you can realize a full subtractor using half subtractors. For the implementation of a full subtractor, we require two half subtractors. Let's start with a brief overview of half and full subtractors.

## What is a Half Subtractor?

A **half-subtractor** is a combinational logic circuit that has two inputs and two outputs where one output is difference bit (d) and another is the borrow bit (b). The half subtractor produces the difference between the two binary bits and also produces a borrow output (if any). In the subtraction (A-B), A is called **Minuend** and B is called **Subtrahend bit.**

The block diagram and logic circuit diagram of the half subtractor are shown in Figure-1.

From the logic diagram of the half subtractor, it can be seen that a half subtractor can be realized using an XOR gate together with a NOT gate and an AND gate.

The difference bit (d) of the half subtractor is given by XORing the two inputs A and B. Therefore,

$$\mathbf{Difference,\:d=A\bigoplus B=A'B+AB'}$$

The borrow (b) of the half subtractor is the AND of A' (compliment of A) and B. Therefore,

$$\mathbf{Borrow\:,\:b=A'B}$$

## What is a Full Subtractor?

A **full subtractor** is also a combinational logic circuit which has three inputs A, B, bin and two outputs "d" and "b". Where, "A" is the minuend bit, "B" is the subtrahend bit, "bin" is borrow produced at the previous stage, d is the output difference bit and b is the output borrow bit.

The block diagram and circuit diagram of a full-subtractor is shown in Figure-2.

From the logic diagram of the full subtractor, we can see that the implementation of a fullsubtractor requires two XOR gates, two NOT gates, two AND gates, and one OR gate.

Now, let us discuss the realization of full subtractor using two half subtractors.

## Implementation of a Full Subtractor using Two Half Subtractors

A full subtractor can be realized using two half subtractors. It will take two half-subtractors and one OR gate. The logic circuit diagram of the full subtractor using two half subtractors is shown in Figure-3.

The first half subtractor performs XOR operation on input bits A and B, and AND operation on A' and B to produce an intermediate borrow bit

The second half subtractor performs the XOR operation on the output of first XOR gate and the input borrow bit $(b_{in})$, and the AND gate of the second half circuit gives an output equal to (A'B+AB')'.$b_{in}.$

The output of the second XOR gate is the output different bit (d), and the output borrow bit (b) is obtained by ORing the outputs of two AND gates.

In this way, we can realize a full subtractor by cascading two half subtractors, as shown in the above figure

- Related Articles
- Realization of a Full Subtractor using NAND gate
- Half Subtractor Using NAND Gates
- Half Subtractor in Digital Electronics
- Full Subtractor in Digital Electronics
- Design Full Adder Using Half Adder
- The Realization of Logic Functions Using NAND Gates
- Difference between Half Adder and Full Adder
- What is Half Duplex mode? Differentiate between half duplex and full duplex?
- Difference between Half Wave and Full Wave Rectifier
- What is Full Duplex mode? Differentiate between simplex, half duplex and full duplex?
- Difference between Simplex, Half duplex and Full Duplex Transmission Modes
- Adders and Subtractors in Digital Electronics
- A railway half ticket costs half the full fare and the reservation charge is the same on half ticket as on full ticket. One reserved first class ticket from Mumbai to Ahmedabad costs Rs. 216 and one full and one half reserved first class tickets cost Rs. 327. What is the basic first class full fare and what is the reservation charge?
- How to plot a half-black and half-white circle using Matplotlib?
- Cascade Form Realization of Continuous-Time Systems