The given FSM has input b, output z, and starts in state x. What is the FSM's resulting output if b is 1 on the first rising clock edge, 1 on the second, and 1 on the third?

Question

BlackTom AI · Accepted Answer

We start by restating the problem and every option clearly to set the stage for analysis.
- Question: The given FSM has input b, output z, and starts in state x. What is the FSM's resulting output if b is 1 on the first rising clock edge, 1 on the second, and 1 on the third?
- Answer options: ["z = 0", "z = 1", "z = 01", "z = 11"]

Now, we examine each option in turn and relate it to the FSM behavior as implied by the diagram and the state table.

Option 1: z = 0
- This option asserts that after the three consecutive b = 1 inputs, the output z ends up being 0.
- In the FSM diagram, the z output is determined by the current state via the combinational logic feeding z. The transitions shown (from the initial state through the intermediate state and the associated red-encoded states) lead to a sequence where z remains 0 across the state updates when b is repeatedly 1. Since the final state reached after three clock edges still maps to z = 0 in the provided encoding, this option is consistent with the table and the state-logic relationship.

Option 2: z = 1
- This would require that, after the three 1s on input b, the FSM ends in a state for which z is 1.
- If the state encoding or the combinational logic in the diagram assigns z = 1 to that final state, this could be plausible only if the final state after three 1s is indeed the one with z = 1. However, the given state-encoding and the transitions shown indicate that the z output remains 0 for the relevant sequence of states when b stays high, so z = 1 contradicts the observed behavior in the diagram.

Option 3: z = 01
- This option suggests a two-bit output over time, i.e., z changing from 0 to 1 across the clock edges, or representing a two-bit vector. The FSM description specifies a single-bit output z (and the options include only single-bit values 0 or 1, or multi-bit patterns that do not align with the single-bit z). Therefore, stating z as 01 is inconsistent with the single-bit output assumption and the table showing z as a single bit.

Option 4: z = 11
- Similar to the previous option, this presents a two-bit pattern for z, which is not compatible with z being a single-bit output in the FSM description and the accompanying table. Hence this is not a valid representation for the single z output after three clock edges.

Putting it together, the only option that aligns with the FSM’s single-bit output behavior and the shown state transitions under three consecutive b = 1 inputs is z = 0. The other options either propose an impossible single-bit value given the final state in the diagram, or incorrectly treat z as a multi-bit signal, which is not supported by the FSM's specification in the figure.

The given FSM has input b, output z, and starts in state x. What is the FSM's resulting output if b is 1 on the first rising clock edge, 1 on the second, and 1 on the third?单项选择题

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