 Solution

state    00    01    11    10    INC
 A        A     B     B     A      0
 B        A     B     B     C      0
 C        I     B     B     C      0
 I        A     B     B     A      1

For a normal entry the states are

A \to B \to B \to C \to I

; retreat after the first sensor instead gives

A \to B \to A

with no pulse. Repeated samples at one sensor remain in the corresponding phase. State

I

always exits on the next edge, so its output lasts exactly one clock period; an outer activation on that next edge goes directly to

B

, allowing the next visitor to start immediately.

This follows the question's single-visitor entry model and merges the two outer-active phases as its hint requests. Inputs are sampled synchronously; the table also specifies deterministic recovery for other sampled combinations. It is not a specification of a bidirectional occupancy counter for arbitrary overlapping entry and exit traffic.

Figure 1.
Four-state visitor-entry Moore machine with a one-clock output pulse
. Original state diagram. Edge labels use $x_{1} x_{0}$ . State I emits the count pulse; its transitions can accept the next visitor without an extra idle clock. **Details**.

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