# Full Subtractor | Definition | Circuit Diagram | Truth Table

## Half Subtractor-

Before you go through this article, make sure that you have gone through the previous article on Half Subtractor.

We have discussed-

• Half Subtractor is used for the purpose of subtracting two single bit numbers.
• Half subtractors have no scope of taking into account “Borrow-in” from the previous circuit.
• To overcome this drawback, full subtractor comes into play. ## Full Subtractor-

• Full Subtractor is a combinational logic circuit.
• It is used for the purpose of subtracting two single bit numbers.
• It also takes into consideration borrow of the lower significant stage.
• Thus, full subtractor has the ability to perform the subtraction of three bits.
• Full subtractor contains 3 inputs and 2 outputs (Difference and Borrow) as shown- ## Designing a Full Subtractor-

Full subtractor is designed in the following steps-

### Step-01:

Identify the input and output variables-

• Input variables = A, B, Bin (either 0 or 1)
• Output variables = D, Bout where D = Difference and Bout = Borrow

### Step-02:

Draw the truth table-

 Inputs Outputs A B Bin Bout (Borrow) D (Difference) 0 0 0 0 0 0 0 1 1 1 0 1 0 1 1 0 1 1 1 0 1 0 0 0 1 1 0 1 0 0 1 1 0 0 0 1 1 1 1 1

### Step-03:

Draw K-maps using the above truth table and determine the simplified Boolean expressions- ### Step-04:

Draw the logic diagram.

The implementation of full adder using 1 XOR gate, 3 AND gates, 1 NOT gate and 1 OR gate is as shown below- To gain better understanding about Full Subtractor,

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Summary
Article Name
Full Subtractor | Definition | Circuit Diagram | Truth Table
Description
Full Subtractor is a combinational logic circuit used for the purpose of subtracting two single bit numbers with a borrow. Full Subtractor Definition, Block Diagram, Truth Table, Circuit Diagram, Logic Diagram, Boolean Expression and Equation are discussed. Full Subtractor overcomes the limitation of Half Subtractor.
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Gate Vidyalay
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