How many possible combinations can be represented by a six-digit binary number?

A six-digit binary number can have each digit set to either 0 or 1. Therefore, for each digit position, there are 2 possible states (0 or 1). To calculate the total number of combinations for a six-digit binary number, you can use the formula for combinations of binary digits, which is given by (2^n), where (n) is the number of digits.

In this case, since there are six digits, the calculation is (2^6). Performing this calculation yields:

[

2^6 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 = 64

]

This means that a six-digit binary number can represent 64 unique combinations. Each combination corresponds to a different arrangement of 0s and 1s across the six positions. This aligns with the choice indicating 64 combinations as the correct answer.

By understanding this process, you can confidently determine the possible combinations for any binary number of varying lengths using the same approach.