BINARY ADDER/SUBTRACTOR

A binary adder-subtractor is a digital circuit that is capable of performing both addition and subtraction operations on binary numbers by including an exclusive-OR gate with each full adder. The circuit takes two binary numbers as inputs and produces a sum or difference as output, depending on the control signal M.

xor operation in the circuit

Why binary adder/subtractor?

• It can perform both addition and subtraction operations on binary numbers using a single circuit.
• This provides a significant advantage in terms of cost and complexity compared to using separate circuits for addition and subtraction.
• Binary adder-subtractors are commonly used in microprocessors, where arithmetic operations on binary numbers are frequently performed.

working of binary adder/subtractor

The control signal M controls the operation. When M = 0, the circuit is an adder, and when M = 1, the circuit becomes a subtractor. Each exclusive-OR gate receives input M and one of the inputs of B.

When M = 0, we have B xor 0 = B. The full adders receive the value ofB , the input carry is 0, and the circuit performs A plus B .

When M = 1, we have B xor 1 = B’ and C0 = 1. The B inputs are all complemented and a 1 is added through the input carry. The circuit performs the operation A plus the 2’s complement of B .

When and where it is used?

1. To perform addition and subtraction operations in microprocessors and other digital circuits.
2. To implement arithmetic operations in digital signal processing algorithms such as Fast Fourier Transform (FFT).
3. To implementing cryptographic algorithms, such as in the design of digital encryption and decryption circuits.

Advantages of binary adder/subtractor

1. Versatility: A binary adder-subtractor is capable of performing both addition and subtraction operations on binary numbers using a single circuit. This makes it a versatile and flexible circuit that can be used in a wide range of applications.

2. Scalability: By cascading multiple full-adder circuits, the binary adder-subtractor can be designed to handle any number of bits, from 4-bit to 64-bit or more.

3. Speed: The binary adder-subtractor is a fast circuit that can perform arithmetic operations on binary numbers in a fraction of a second. This makes it well-suited for applications that require real-time processing of binary data.

4. Efficiency: The binary adder-subtractor is an efficient circuit that uses minimal power and occupies a small amount of space on a microchip. This makes it an ideal circuit for use in battery-powered devices and other applications where power consumption and space are critical.

Disadvantages of binary adder/subtractor

1. Limited functionality: it cannot perform other arithmetic operations such as multiplication and division. For these operations, separate circuits are required.

2. Complexity: circuit is complex to design and implement, especially when handling larger binary numbers. This can increase the cost and development time of a project.

3. Error propagation: If an error occurs in one of the full-adder circuits in a binary adder-subtractor, it can propagate through the circuit and cause errors in the final output.