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.

1. nk − nk = 2. In this case, the output at the k -th and all subsequency clock ticks is 10.

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

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

(A) 5

(B) 6

(C) 7

(D) 8

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