Arithmetic Circuits

Arithmetic circuits are combinations of digital logic gates and other electronic components that are used to perform one or more arithmetic operations like addition, subtraction, multiplication, division , store and process the results.

• Combinational circuits perform arithmetic operations based on the input values, whereas sequential circuits use feedback to perform arithmetic operations. For example, a half adder is a combinational circuit that can add two single-digit binary numbers, while a full adder is a combinational circuit that can add two multi-digit binary numbers.

• Sequential arithmetic circuits, on the other hand, use registers, flip-flops, and other storage elements to store intermediate values during computation. One example is counter a sequential circuit that increments a binary value each time a clock signal is received. They enable complex mathematical operations to be performed quickly and accurately.

Why can't we design an arithmetic circuit using either combinational or sequential circuit?

• Combinational circuits can perform arithmetic operations such as addition, subtraction, multiplication quickly and efficiently, but they are limited in their ability to store and process intermediate results.

• Sequential circuits, on the other hand, are capable of storing and processing intermediate results , implement operations such as shifting, counting, control the operation of the combinational circuit, and coordinate the timing of the circuit hence making them more versatile and flexible than combinational circuits.

• Consider the following example: A 32 bit adder is implemented by feeding 32 bit inputs A and B into their respective input shift registers. Each input shift register shifts one bit into the adder and the adder performs bit-wise addition for 32 clock cycles. The resultant sum is shifted into the output shift register. Therefore, arithmetic circuits require both combinational and sequential circuits to operate correctly.

Applications

1. Digital signal processing is used to analyze and manipulate signals. For example, in a digital filter, the input signal is processed by a series of arithmetic operations, which are performed using shift registers, multipliers, and adders.

2. Computer arithmetic Arithmetic circuits using sequential circuits are used in the arithmetic units of computer processors to perform addition, subtraction, multiplication, and division operations. For example a sequential multiplier is used to compute the product of two numbers including shift register being a sequential circuit and a sequential adder used to accumulate the result.

3. Cryptography: used to encrypt and decrypt data. For example to perform the modular operation in RSA algorithm.