The basic building blocks of the arithmetic unit in digital computers are Adders.

Explanation:
The arithmetic unit is a crucial component of a digital computer that performs various arithmetic operations such as addition, subtraction, multiplication, and division. It is responsible for executing arithmetic instructions and manipulating numerical data.

The basic building block of the arithmetic unit is the adder, which is a combinational logic circuit. It is designed to perform binary addition of two binary numbers. The adder takes two binary inputs and produces a sum output and a carry output. The sum output represents the result of the addition, while the carry output indicates if there is an overflow.

Functionality of an Adder:
An adder can be built using basic logic gates such as AND, OR, and XOR gates. There are different types of adders, including half adders, full adders, ripple carry adders, carry lookahead adders, and carry-select adders. Each type has its own advantages and trade-offs in terms of speed, complexity, and power consumption.

- Half Adder: A half adder is the simplest form of an adder that takes two binary inputs (A and B) and produces two outputs: sum (S) and carry (C). It does not consider any carry input from previous stages.

- Full Adder: A full adder is an extension of the half adder that takes three binary inputs: A, B, and a carry input (Cin). It produces two outputs: sum (S) and carry (Cout). The carry input (Cin) accounts for any carry generated from previous stages.

- Ripple Carry Adder: A ripple carry adder is built by cascading multiple full adders together. The carry output from each full adder is connected to the carry input of the next full adder. This allows the adder to handle addition of multi-bit binary numbers.

- Carry Lookahead Adder: A carry lookahead adder is a more advanced adder that reduces the propagation delay associated with ripple carry adders. It uses additional logic to generate carry signals in parallel, resulting in faster addition.

- Carry-Select Adder: A carry-select adder is a high-speed adder that uses multiple ripple carry adders and a multiplexer to perform addition. It allows for parallel computation of different combinations of carry inputs, selecting the correct result based on the actual carry input.

Conclusion:
In summary, the adder is the fundamental building block of the arithmetic unit in digital computers. It performs binary addition and is used in various arithmetic operations. Different types of adders exist, each with its own advantages and trade-offs in terms of performance and complexity.