Question 7 of 7: Combinational Logic Design — Subway Door Control

Question 7: Combinational Logic Design — Subway Door Control (20 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

Given. Seven binary sensors A–G (train moving, doors open, at station, open-button, close-button, obstruction, signal-green) and the stated open/close business rules, including the two "no action if already in that state" guards.

Find. The OPEN truth table and gate design (parts a, c), and the CLOSE truth table and gate design (parts b, d).

Approach. Translate each English rule directly into a Boolean AND of literals (complementing wherever the rule says "not" or "already"), then read the truth table straight off that single product term — a 1-minterm function needs only an AND gate with the appropriate input inversions, no simplification required.

1. OPEN logic (parts a, c). Doors open when: not moving ($A'$), at a station ($C$), open button pressed ($D$), AND doors not already open ($B'$, the "no action if already open" guard): $$ OPEN = \boxed{A'\cdot B'\cdot C\cdot D}. $$ Sensors E, F, G do not appear in OPEN — the close-side rules do not gate the open function.
2. CLOSE logic (parts b, d). Doors close when: currently open ($B$, the "no action if already closed" guard), close button pressed ($E$), signal green ($G$), AND no obstruction ($F'$): $$ CLOSE = \boxed{B\cdot E\cdot F'\cdot G}. $$ A and C/D do not appear — closing is independent of train motion/station/open-button state once the door is open and the close button is pressed.