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?

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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.

S2501-CPSC-3300-001-11767 Exam 1

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?

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