Question

after the fourth clock pulse, a 4 - bit johnson sequence is q0 = 0, q1 = 1, q2 = 1, and q3 = 1. after the fifth clock pulse, the sequence is ______. q0 = 0, q1 = 0, q2 = 0, q3 = 1 o q0 = 1, q1 = 1, q2 = 1, q3 = 0 o q0 = 0, q1 = 0, q2 = 1, q3 = 1 o q0 = 1, q1 = 0, q2 = 0, q3 = 0 o

Explanation:

Step1: Recall Johnson counter operation

In a Johnson counter, the output of the last - stage flip - flop is fed back to the input of the first - stage flip - flop in an inverted form.

Step2: Analyze the given state

Given the state after the fourth clock pulse as $Q_0 = 0, Q_1 = 1, Q_2 = 1, Q_3 = 1$. The input to $Q_0$ for the fifth clock pulse is the inverted value of $Q_3$. Since $Q_3 = 1$, the input to $Q_0$ is $0$. Then, all the other bits shift left. So $Q_1$ takes the previous value of $Q_0$ (which is $0$), $Q_2$ takes the previous value of $Q_1$ (which is $1$), and $Q_3$ takes the previous value of $Q_2$ (which is $1$).

Answer:

$Q_0 = 0, Q_1 = 0, Q_2 = 1, Q_3 = 1$