Full Subtractor | Truth Table, Implementation

By Priyanshu Vaish|Updated : May 20th, 2022

This article deal with the full subtractor. The full subtractors are generally employed for ALU (Arithmetic Logic Unit) in computers to subtract as CPU & GPU for the applications of graphics to decrease the circuit difficulty.

The full subtractor is the combinational circuit to perform subtraction using 3 bits. Subtractors are mostly used for performing arithmetic functions like subtraction in digital devices and electronic calculators.

Table of Content

What is a Full Subtractor?

A full subtractor is an arithmetic circuit that performs a subtraction between two bits, considering that a lower significant stage may have borrowed a '1'. Thus a full subtractor has three inputs and two outputs. The full subtractor block diagram is shown below.


Truth Table of Full Subtractor

The two inputs are A and B, and the third input is input as C. The output carry is designated as b(borrow), and the normal output is designated as d, which is the difference. The truth table of a full subtractor is represented as given below:


Output Equation of Full Subtractor

From the above truth table, the map for the outputs of the full subtractor is shown below, and the logical expression for the difference and borrow is as below:



Implementation of Full Subtractor Circuit

From the above expression, a full subtractor circuit can be realized in SOP form or with two half subtractors and an OR gate, as shown below:


The ANSI/IEEE standard logic diagram of the full subtractor is shown below:


The full subtractor can also be realized using a universal logic gate that is either only NAND gates or only NOR gates. The total number of NAND gates/Nor gates required to implement a full subtractor equals "9".


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FAQs on Full Subtractor

  • A full subtractor is the combinational circuit that performs the subtraction of two bits. One is the minuend, and the other is subtrahend, taking into account the borrow of the previous adjacent lower minuend bit.

  • The full subtractor produces 2 outputs borrow and difference. A full subtractor has 3 input bits and two outputs bits borrow and difference. The full subtractor can be implemented using two half subtractors and an OR gate.

  • When designed from truth tables and K-maps, a full subtractor is very similar to a full adder, but it contains two inverters that a full adder does not. When configured to subtract, an adder/subtractor circuit adds a single inverter (in the form of an XOR gate) to one input of a full adder module.

  • The difference between a half subtractor and a full subtractor is the output of the half subtractor is the Ex-OR of two inputs. However, the difference output of the full subtractor is Ex-OR of three inputs.

  • Generally, the full subtractor is one of the most used and essential combinational logic circuits. It is a basic electronic device used to perform the subtraction of two binary numbers.

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