GATE | GATE-CS-2003 | Question 90

A 1-input, 2-output synchronous sequential circuit behaves as follows : Let zk, nk denote the number of 0\'s and 1\'s respectively in initial k bits of the input (zk + nk = k). The circuit outputs 00 until one of the following conditions holds.

    zk - nk = 2. In this case, the output at the k-th and 
                 all subsequent clock ticks is 10.
    nk - zk = 2. In this case, the output at the k-th and
                 all subsequent clock ticks is 01.

What is the minimum number of states required in the state transition graph of the above circuit?

(A)

(B)

(C)

(D)