Given an array of integers of size 5 , how does the computer know where the \( 3^{\text {rd }} \) indexed variable is located? It remembers where all the indexed variables of the array are located. It adds 3 to the base address of the array. none of these It adds space for 3 integers to the base address of the array.

In computer memory, arrays are stored as contiguous blocks of memory. To access the \( i^{\text{th}} \) element in an array, the computer uses the base address of the array and calculates the address of the desired element by adding an offset based on the size of each element and its index. Here's how it works step-by-step: 1. **Base Address**: This is the starting address of the array in memory. 2. **Element Size**: Each element in the array (e.g., an integer) occupies a fixed number of bytes. For example, if an integer takes up 4 bytes, the size \( s \) is 4. 3. **Index Calculation**: To find the address of the \( i^{\text{th}} \) element, multiply the index \( i \) by the size \( s \) and add it to the base address: \[ \text{Address of } a[i] = \text{Base Address} + (i \times s) \] For the \( 3^{\text{rd}} \) indexed element (assuming zero-based indexing), the calculation would be: \[ \text{Address of } a[3] = \text{Base Address} + (3 \times s) \] **Option Analysis:** - **It remembers where all the indexed variables of the array are located.** This is incorrect because the computer doesn't store each element's address separately; it uses the base address and calculates each address on the fly. - **It adds 3 to the base address of the array.** This is incorrect because it doesn't account for the size of each element. Simply adding 3 would not correctly calculate the offset unless the size of each element is 1 byte. - **None of these** This is incorrect because one of the options is actually correct. - **It adds space for 3 integers to the base address of the array.** **This is correct.** It means the computer adds \( 3 \times \text{size of an integer} \) to the base address to find the address of the \( 3^{\text{rd}} \) indexed element. **Final Answer:** It adds space for 3 integers to the base address of the array.