Adders are used in various parts of a processor to perform arithmetic calculations. The correct answer is option 'D', which states that adders are used to calculate addresses, table indices, and increment and decrement operators. Let's explore each of these in detail:

1. Addresses:
In a processor, addresses are used to access data from memory or registers. Adders are used to perform address calculations, such as adding an offset to a base address or calculating the next memory address in a sequence. By using adders, the processor can efficiently calculate the desired address for fetching or storing data.

2. Table indices:
In many cases, processors use tables or arrays to store data. To access a specific element in a table, the processor needs to calculate the index of the desired element. Adders can be used to perform this calculation by adding the base address of the table with an offset or an index value. The result obtained from the adder is used to access the desired element in the table.

3. Increment and decrement operators:
Processors often need to increment or decrement the value of a variable or a memory location. Adders can be used to perform these operations efficiently. For example, to increment a value by one, the processor can use an adder to add the value with 1. Similarly, to decrement a value by one, the processor can use an adder to subtract 1 from the value.

By incorporating adders in different parts of the processor, these arithmetic calculations can be performed efficiently and quickly. Adders are a fundamental component of the arithmetic logic unit (ALU) in a processor. They can perform addition, subtraction, and other basic arithmetic operations, making them an essential part of the processor's functionality.

In conclusion, adders are used in various parts of a processor to calculate addresses, table indices, and perform increment and decrement operations. They play a crucial role in enabling efficient arithmetic calculations within the processor.