A bunch of computer scientists take over an island and start their own country. They want the license plates to use binary numbers. There's space for 7 digits on each license plate and the first plate starts at \[0000000\].

Question

How many unique license plates can their country support?
Answer in decimal:

Answer 1

Each license plate consists of 7 binary digits. In binary, each digit can be either 0 or 1. Therefore, for each of the 7 digits, there are 2 possible choices (0 or 1).

To determine the total number of unique license plates, we calculate the number of combinations of 7 binary digits. This is given by:

\[ 2^n \]

where \( n \) is the number of digits. In this case, \( n = 7 \):

\[ 2^7 = 128 \]

Thus, the total number of unique license plates that can be created with 7 binary digits is:

\[ \boxed{128} \]