Full Subtractor and Half Subtractor
A Binary Subtractor is a digital circuit that performs the arithmetic binary subtraction between two numbers with respect to the logic operations and laws of Boolean Algebra.
The subtractors are used in combinational circuit design and the Arithmetic Logic Unit (ALU) of the processor to calculate multiple addresses. Subtractor circuits reduce sound distortion in amplifiers and the power of radio signals.
There are two types of Subtractor circuits-
- Half Subtractors
- Full Subtractors
Half Subtractor in Digital Electronics
A half subtractor is a digital logic circuit that performs binary subtraction of two single-bit binary numbers. It has two inputs, A and B, and two outputs, DIFFERENCE and BORROW. The DIFFERENCE output is the difference between the two input bits, while the BORROW output indicates whether borrowing was necessary during the subtraction.
The half subtractor can be implemented using basic gates such as XOR and NOT gates. The DIFFERENCE output is the XOR of the two inputs A and B, while the BORROW output is the NOT of input A and the AND of inputs A and B.
Truth Table for Half Subtractor
The SOP form of the Diff and Borrow is as follows:
Diff= A’B+AB’
Borrow = A’B
Circuit Diagram of Half Subtractor
Application of Half Subtractor
- Calculators
- Alarm Frameworks
- Automotive Industry
- Security Applications
- Computer Devices
Full Subtractor in Digital Electronics
A full subtractor is a combinational circuit that performs subtraction of two bits.
This circuit has three inputs and two outputs.
For three single-bit binary numbers A, B, and P, the full subtractor circuit generates two single-bit binary outputs D (Difference), and Q (Borrow Output).
A full Subtractor was made to overcome the limitations of a Half Subtractor.
The complete subtractor circuit can be obtained by using two half subtractors with an extra OR gate.
The full subtractor block diagram is shown below
Here A is minuend, B is subtrahend & Bin is Borrow in. The outputs are Difference (Diff) & Bout (Borrow out).
Truth Table
Logical expression for difference
D = (A XOR B) XOR Bin
Logical expression for borrow
Bout = A’Bin + A’B + BBin
Circuit Diagram for Full Subtractor
Applications of Full Subtractors are used in
- Performing Arithmetical functions like subtraction in ALU of Microprocessors.
- Electronic Calculators
- Digital Devices
- Computing Address Tables in ALU.
- DSP and networking-based systems.
