Changing only open width moves the half-open capture boundary. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Two-second width ends exactly at the arrival and blocks

Open start stays 4 s and arrival stays 6 s. Width 2 s makes end 6 s, so the latch gate is block and output is 0.

4+2=6,664+2=6,\quad 6\not<6
Latch open-width scanThe half-open endpoint moves with width.window [4, 6) sarrival 6 sD 1Q 0blocked

Three-second width includes the same arrival

Open start stays 4 s and arrival stays 6 s. Width 3 s makes end 7 s, so the latch gate is capture and output is 1.

4+3=7,46<74+3=7,\quad 4\le 6<7
Latch open-width scanThe half-open endpoint moves with width.window [4, 7) sarrival 6 sD 1Q 1captured

Four-second width keeps the capture safely inside

Open start stays 4 s and arrival stays 6 s. Width 4 s makes end 8 s, so the latch gate is capture and output is 1.

4+4=8,46<84+4=8,\quad 4\le 6<8
Latch open-width scanThe half-open endpoint moves with width.window [4, 8) sarrival 6 sD 1Q 1captured