Digital Electronics Decoded: The Function of Subtractors

by Yuvi K - December 16, 2023

Digital Electronics Decoded: Exploring the Function of Subtractors

The world of digital electronics plays a major role in our day-to-day lives. Digital electronics is the basis of almost every electronic device, from computers and phones to robots and self-driving cars. It powers our lives and offers countless possibilities.

In order to understand the inner workings of digital electronics, many concepts must be explored. One such concept is subtractors, which are electronic circuits that are used in digital systems. In this article, we will discuss the function of subtractors and how they operate.

What is a Subtractor?

A subtractor is an electronic circuit that subtracts two digital inputs and provides the difference as the output. It is a type of digital circuit that performs subtraction between two binary numbers using the principles of Boolean algebra. Subtractors can be either active – meaning they contain a transistor – or passive – they contain no transistors.

How Does a Subtractor Work?

Subtractors use a simple formula to perform subtraction. This formula is based on the principles of Boolean Algebra and is as follows:

A-B=A’+B

In this formula, A and B represent the two binary numbers, and A’ is the complement of A (the opposite of the number A).

The basic structure of a subtractor circuit consists of three inputs: the first two are A and B, and the third is a control line C (also known as an enable line). This control line is used to control the operation of the subtractor.

When the control line C is active (set to logic 1), the subtractor performs the subtraction A-B. When the control line C is de-activated (set to logic 0), the subtractor gets disabled and performs no subtraction.

Types of Subtractors

Subtractors can be of the following types:

Half Subtractor:
A half subtractor is a simpler version of a subtractor circuit and only allows subtracting of two single bits. It contains two inputs, A and B, and one output D (difference), computed according to the formula A-B. The half subtractor requires a control line C for subtraction to occur.

Full Subtractor:
A full subtractor is an advanced version of the half subtractor. It has three input bits, A, B and C, and two output bits, D (difference) and B (borrow). It subtracts two binary numbers and also determines if there is a “borrow” in the subtraction, which occurs when the subtrahend is greater than the minuend.

Multi-Bit Subtractor:
A multi-bit subtractor is a subtractor circuit that can subtract multiple bits (for example, 8 bits). It contains two inputs, A and B, and one output D, computed according to the formula A-B. The multi-bit subtractor requires a control line C for subtraction to occur.

Difference Between Half Subtractor and Full Subtractor

The following table summarizes the differences between a half subtractor and a full subtractor:

Applications of Subtractors

Subtractors are used in a variety of digital electronic devices. They are used in digital clocks, calculators, counters, adders, computers, and even robots. They are also used in signal processing, commercial transaction processing, data compression, computer-aided design, and encryption.

Conclusion

Subtractors are one of the most important components of digital electronics. They are used to subtract two digital inputs and generate the difference as the output. They come in three forms: half subtractors, full subtractors and multi-bit subtractors. Subtractors are used in many digital applications, such as computers, robots and signal processing.

Understanding the function of subtractors is important for anyone who works with digital electronics. With the right knowledge of subtractors, you will be able to develop efficient digital systems that can power anything from digital clocks to robotic arms.