Final answer:
With 26 bits, there are 2^26 or 67,108,864 unique memory locations that can be addressed. This is based on each bit having two possible states.
Step-by-step explanation:
How Many Unique Memory Locations Can Be Addressed?
When considering memory in computers, specifically how many unique locations can be addressed with 26 bits, you can use principles from Mathematics and Information Theory. Each bit has two possible values: a 0 or a 1. Therefore, with 26 bits, the number of unique addresses that can be generated is 2 to the power of 26. This is analogous to having 26 binary decisions, where each decision allows you to choose between two options, leading to 2^26 possible combinations. When computed, this yields 67,108,864 unique memory locations that can be addressed.
The number of locations that can be addressed uniquely with 26 bits available for each word of memory can be calculated by raising the number of possibilities in one iteration (which is 2 to the power of 26) to the power of the number of words of memory. In this case, we have 5 words of memory, so the calculation would be 2^26 x 2^26 x 2^26 x 2^26 x 2^26, which simplifies to 2^(26x5) or 2^130. Therefore, there can be 2^130 unique memory locations that can be addressed.