A 4-bit ring counter is initialized to 1000. How many distinct states does it traverse in its normal one-hot cycle?
A 4-bit ring counter cycles through four one-hot states.
A 4-bit Johnson counter has how many distinct states in its normal cycle?
An n-bit Johnson counter has 2n states; for $n=4$, that is 8.
A 4-bit Johnson counter has how many unused states out of 16 possible binary states?
$It uses 2n=8 states, leaving 16-8=8 unused states.$
An asynchronous (ripple) 4-bit binary up-counter uses flip-flops with propagation delay $t_{pd}$ = 25 ns each. What is the maximum operating clock frequency $f_{max}$ of the counter?
Total ripple delay = 4 * $t_{pd}$ = 4 * 25 ns = 100 ns. Maximum frequency $f_{max} = 1 / 100 ns = 10 MHz$.
How many flip-flops are required to construct a MOD-125 counter?
Since $2^6$<125$\le 2^7, seven flip-flops$ are required.