15.20 The following are possible state assignments for a six-state sequential circuit.(i)(ii)(iii) (iv) (v)So000010100110 001S₁001111101010111S₂010001000111 1015301111000101101154100000111 000 000S5 101 100 110 100 010(a) Which two state assignments are equivalent?(b) For each assignment (except (i)), give an equivalent assignment for which stateSo is assigned to 000.(c) Give a state assignment which is not equivalent to any of the assignments.

Sequential circuit is a special type of circuit which consists of different inputs and outputs. In this kind pf senario the output of the system generally depends on the current as well as the previous inputs given.Now as per the question the given assignment for the six-state sequential circuit is In order to determine the equivalent two states assignments, it is necessary to compare each pair of the assignments. The two states of the pair of assignments will only be equivalent if the next state and the output are same for every given input. Now let us compare the next state of each of the assignmentsfor (i) the next states are Next_S0 : 001N_S1 : 010N_S2 : 011N_S3 : 100N_S4 : 101N_S5 : 000for (ii) the next states areNext_S0 : 111N_S1 : 001N_S2 : 110N_S3 : 000N_S4 : 100N_S5 : 010Similarly by evaluating (iii) we get Next_S0 : 101N_S1 : 000N_S2 : 001N_S3 : 111N_S4 : 110N_S5 : 100next states of (iv)Next_S0 : 010N_S1 : 111N_S2 : 011N_S3 : 000N_S4 : 100N_S5 : 110next states of (v)Next_S0 : 111N_S1 : 010N_S2 : 111N_S3 : 101N_S4 : 011N_S5 : 000So we can say that no pair of assignments are equivalent to each other.Assignment (ii)The equivalent assignment for which S0=000 can be obtained by shifting all the states to the rightS0: 000S1: 010S2: 111S3: 001S4: 110S5: 000Assignment (iii)The equivalent assignment for which S0=000 can be obtained by rotating all the states to the rightS0: 000S1: 100S2: 101S3: 000S4: 001S5: 111Assignment (iv)The equivalent assignment for which S0=000 can be obtained by shifting all the states to the leftS0: 000S1: 110S2: 010S3: 111S4: 011S5: 000 Assignment (v)The equivalent assignment for which S0=000 can be obtained by inverting the order of the states given.S0: 000S1: 010S2: 111S3: 010S4: 111S5: 101Let's explore a new assignment to provide a state assignment that is not comparable to any of the assignments.S0 : 011S1 : 110S2 : 101S3 : 000S4 : 111S5 : 001We can say that this assignment is different from all the assignments given.(a) Upon evaluating we get that no pair of the assignments are equivalent.(b) The condition for which the equation is equivalent is mentioned above.(c) The assignment which is not equivalent to each of the given assignments isS0 : 011S1 : 110S2 : 101S3 : 000S4 : 111S5 : 001