Half Subtractor and Full Subtractor
Subtractor Circuit (Digital Electronics)
A subtractor circuit is a combinational logic circuit used to perform the subtraction of binary numbers. It produces two outputs called Difference and Borrow. Subtractor circuits are widely used in digital systems, processors, and arithmetic logic units (ALU).
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1. Half Subtractor
A half subtractor is a combinational logic circuit that subtracts one single-bit binary number from another. It has two inputs and produces two outputs called Difference and Borrow.
Inputs and Outputs
- Inputs: A (minuend), B (subtrahend)
- Outputs: Difference (D), Borrow (Bo)
Logic Expressions
- Difference: \( D = A \oplus B \)
- Borrow: \( B_o = \overline{A}\,B \)
Truth Table of Half Subtractor
| A | B | Difference (D) | Borrow (Bo) |
|---|---|---|---|
| 0 | 0 | 0 | 0 |
| 0 | 1 | 1 | 1 |
| 1 | 0 | 1 | 0 |
| 1 | 1 | 0 | 0 |
Logic Diagram Description
The half subtractor can be implemented using:
- An XOR gate to generate the Difference output
- A NOT gate and an AND gate to generate the Borrow output
Limitations of Half Subtractor
- Cannot handle borrow input from previous stage
- Not suitable for multi-bit subtraction
- Used only for basic understanding
2. Full Subtractor
A full subtractor is a combinational logic circuit that performs subtraction of three binary inputs: two bits and a borrow input from the previous stage. It produces two outputs — Difference and Borrow out.
Inputs and Outputs
- Inputs: A, B, Borrow-in (Bin)
- Outputs: Difference (D), Borrow-out (Bout)
Logic Expressions
- Difference : \( D = A \oplus B \oplus B_{in} \)
- Borrow : \( B_{out} = \overline{A}B + \overline{(A \oplus B)}\,B_{in} \)
Truth Table of Full Subtractor
| A | B | Bin | Difference (D) | Borrow (Bout) |
|---|---|---|---|---|
| 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 1 | 1 |
| 0 | 1 | 0 | 1 | 1 |
| 0 | 1 | 1 | 0 | 1 |
| 1 | 0 | 0 | 1 | 0 |
| 1 | 0 | 1 | 0 | 0 |
| 1 | 1 | 0 | 0 | 0 |
| 1 | 1 | 1 | 1 | 1 |
Implementation of Full Subtractor
A full subtractor can be implemented using two half subtractors and one OR gate. The borrow outputs from the half subtractors are combined using an OR gate to produce the final borrow output.
Video Explanation: Half Subtractor & Full Subtractor
Watch the video below to understand truth tables, logic expressions, and working of half and full subtractors in a simple and visual way.
Quick Summary
| Feature | Half Subtractor | Full Subtractor |
|---|---|---|
| Number of inputs | 2 | 3 |
| Borrow input | No | Yes |
| Outputs | Difference, Borrow | Difference, Borrow |
| Logic gates used | XOR, NOT, AND | XOR, AND, OR, NOT |
| Used in | Basic subtraction | Multi-bit subtraction circuits |
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