Full Subtractor

By Priyanshu Vaish|Updated : November 6th, 2022

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 mainly used for performing arithmetic functions like subtraction in digital devices and electronic calculators. Here, we will see what is a full subtractor in detail, along with its truth table and implementation.

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Table of Content

What is a Full Subtractor?

A full subtractor is an arithmetic circuit that performs a function of "subtraction between two bits", considering that a lower significant stage may have borrowed a '1'. The Full Subtractor is one of the high-scoring concepts for the GATE exam. A full subtractor has three inputs and two outputs.

The full subtractor block diagram is shown below.

Full Subtractor

Full Subtractor Truth Table

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

Truth table of full subtractor

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Full Subtractor Equation

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:

output of full subtractor

Full Subtractor Expression

Full Subtractor EQ

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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:

Circuit Diagram of Full Subtractor

Full subtractor circuit

Full Subtractor Logic Diagram

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

Full subtractor diagram

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

Important Topics for Gate Exam
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Delta Wye TransformationDifference Between Synchronous And Asynchronous Counter
Direct StressDuctile Material
Elastic ConstantsEntity Set in DBMS
Equilibrium of Rigid BodyFactor of Safety


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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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