To determine the base of a binary number, you need to count the number of unique digits used in the binary representation. In binary, there are only two unique digits: 0 and 1. Therefore, the base of a binary number is always 2.
Binary numbers are represented in base-2 because they use a positional numbering system where each digit’s position represents a power of 2. The rightmost digit represents 2^0 (which is 1), the next digit to the left represents 2^1 (which is 2), the next represents 2^2 (which is 4), and so on. This is in contrast to the decimal system, which is base-10, where each digit’s position represents a power of 10.
So, to find the base of any binary number, simply recognize that it’s always 2 because binary consists of only two unique digits: 0 and 1.