You have a 4-bit binary counter with a clock input of 1 MHz. Calculate the time it takes for the counter to cycle through all its states and return to the initial state.
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A 4-bit binary counter can have a maximum of 2^4 = 16 states (from 0000 to 1111).
To calculate the time it takes for the counter to cycle through all its states, we need to determine the time taken for each state. Since the clock input has a frequency of 1 MHz (1 million cycles per second), we can calculate the time taken for each state as:
Time taken for each state = 1 / clock frequency
= 1 / 1 MHz
= 1 microsecond
Since there are 16 states in total, the time it takes for the counter to cycle through all its states and return to the initial state is:
Total time = Time taken for each state * Number of states
= 1 microsecond * 16
= 16 microseconds