What are the commonly used arithmetic circuits?

* Question

What are the commonly used arithmetic circuits?

* Answer

Arithmetic circuits are fundamental components of digital systems used to perform mathematical operations on binary numbers.
They are widely used in microprocessors, digital signal processors (DSPs), and arithmetic logic units (ALUs).

When classified by function, the commonly used arithmetic circuits include the following types:

1. Half Adder

Function:

Performs the addition of two single-bit binary numbers.

Inputs: A, B

Outputs:

Sum (S) = A ⊕ B

Carry (C) = A · B

Characteristics:

Can add only two bits at a time.

Does not handle carry input from previous stages.

Used as the building block of a full adder.

2. Full Adder

Function:

Performs the addition of three binary bits — two operands and one carry input.

Inputs: A, B, Cin

Outputs:

Sum (S) = A ⊕ B ⊕ Cin

Carry (Cout) = (A · B) + (B · Cin) + (A · Cin)

Characteristics:

Can handle carry propagation.

Several full adders can be cascaded to create multi-bit adders (e.g., 4-bit, 8-bit).

3. Half Subtractor

Function:

Performs subtraction of two single-bit binary numbers.

Inputs: A, B

Outputs:

Difference (D) = A ⊕ B

Borrow (B_out) = A′ · B

Characteristics:

Subtracts B from A.

Does not handle borrow input.

4. Full Subtractor

Function:

Performs subtraction of two binary bits with a borrow input.

Inputs: A, B, Bin

Outputs:

Difference (D) = A ⊕ B ⊕ Bin

Borrow (B_out) = (A′ · B) + (Bin · A′) + (Bin · B)

Characteristics:

Used in multi-bit subtraction circuits by cascading full subtractors.

5. Parallel Adder (Ripple-Carry Adder)

Function:

Adds two multi-bit binary numbers using a chain of full adders.
Each stage handles one bit, and the carry ripples from the least significant bit (LSB) to the most significant bit (MSB).

Characteristics:

Simple and easy to design.

Slower due to carry propagation delay.

Example: 4-bit or 8-bit ripple-carry adder.

6. Carry Look-Ahead Adder

Function:

Improves addition speed by predicting carry signals in advance instead of waiting for ripple propagation.

Characteristics:

Much faster than ripple-carry adders.

Used in high-speed processors.

7. Arithmetic Logic Unit (ALU)

Function:

A combinational circuit that performs multiple arithmetic and logical operations, such as:

Addition, subtraction, increment, decrement

AND, OR, XOR, NOT operations

Characteristics:

Central component of microprocessors.

Controlled by operation-select signals.

Can be expanded to perform multiplication, division, and shift operations.

8. Multiplier Circuit

Function:

Performs binary multiplication using a combination of adders and logic gates.

Types:

Array multiplier (uses multiple adders for partial products)

Booth multiplier (efficient for signed numbers)

Applications:

Digital signal processing (DSP), image processing, and embedded systems.

9. Divider Circuit

Function:

Performs binary division through repeated subtraction or shift-based algorithms.

Types:

Restoring division

Non-restoring division

Characteristics:

More complex and slower than multiplication.

Used in CPUs and floating-point units.

10. Incrementer / Decrementer

Function:

Adds or subtracts one from a binary number.

Characteristics:

Simplified version of an adder/subtractor.

Used in counters, program counters (PCs), and address generation.

Summary Table

Conclusion

The commonly used arithmetic circuits include adders, subtractors, multipliers, dividers, and ALUs.
These circuits form the foundation of all digital computation, enabling processors and digital systems to perform mathematical operations efficiently.