Ham Amateur Radio Technician Practice Exam

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How many states does a 3-bit binary counter have?

The correct answer is: 8

A 3-bit binary counter can represent a variety of states given its ability to store binary data. Each bit in a binary number can either be a 0 or a 1. Therefore, for a counter with n bits, the total number of different states it can represent is calculated using the formula 2^n. In this case, with n equal to 3, the calculation is 2^3. This yields a total of 8 unique states, ranging from 000 to 111 in binary, which corresponds to the decimal numbers 0 through 7. Each unique combination of bits represents a different state the counter can be in. This principle of binary counting is fundamental in digital electronics, especially in designing circuits and systems that utilize binary data for storage and processing.