Question: Consider a modulo 4 two-bit up-down counter with input I. I=1 causes the count to increment, e.g., 00->01->10->11, cycling back to 00 from state 11
Consider a modulo 4 two-bit up-down counter with input I. I=1 causes the count to increment, e.g., 00->01->10->11, cycling back to 00 from state 11 (in other words, counting from 0 up to 3 repeatedly). I=0 causes the count to decrement, e.g., 11->10->01->00, cycling back to 11 from state 00. The output values (Q1(t+1) and Q0(t+1)) will always be the same as the next state (S1(t+1) and S0(t+1)) for this device.
The state transition diagram for this device is shown below:

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