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?

Question

Multiple choice

Reveal answer Fill a bubble to check yourself

Explanation

The sequential circuit has 3 variables to decide the state in which input & 2 inputs are present. Output for particular inputs decide states.

i/p	op 1	op 2	State
0	0	0	Initial
0	0	1	$n_k - z_k = 2$
0	1	0	$z_k - n_k = 2$
1	0	0	Not applicable
1	0	0	Initial
1	0	1	$n_k - z_k = 2$
1	1	0	$z_k - n_k = 2$
0	0	1	$n_k - z_k = 2$
1	1	1	is correct

using 3 bits we require $ 2^3 - 1 = 7 $ states here

Answer 1

C Correct answer

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