Combinational Logic — Two-Floor Elevator Control: 04-BS-4, May 2018, Q7

Question 7: Combinational Logic — Two-Floor Elevator 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. Eight binary sensors $A$–$H$ as defined above; corridor buttons ($D$,$E$) are valid only when the car is empty ($A'$); in-car buttons ($F$,$G$) are valid only when occupied ($A$); no action is ever taken unless the doors are closed ($H$); at most one sensor changes at a time.

Find. (a) the logic that starts the elevator moving from the 1st to the 2nd floor on a 2nd-floor corridor call; (b) the logic that acts correctly on either in-car button.

Approach. Each output is a single AND term gating the relevant call/button signal with the required floor sensor, the doors-closed sensor $H$, and (for corridor calls) $A'$ or (for in-car buttons) $A$ — matching exactly the disable rules stated in the question.

a) 1st→2nd movement on a 2nd-floor corridor call. The car must be empty (corridor control only active when $A'$), currently on the 1st floor ($B$), doors closed ($H$), and the 2nd-floor corridor button pressed ($E$): $$UP = B\cdot E\cdot H\cdot A'$$

UP = B . E . H . A' (corridor call, empty car, 1st floor -> 2nd)

b) Action from an in-car button. In-car buttons are active only when occupied ($A$) and doors are closed ($H$); pressing the "2nd floor" button ($G$) while on the 1st floor ($B$) should move the car up, and pressing the "1st floor" button ($F$) while on the 2nd floor ($C$) should move it down: $$UP_{incar}=A\cdot B\cdot H\cdot G \qquad\qquad DOWN_{incar}=A\cdot C\cdot H\cdot F$$

UP_incar = A . B . H . G (occupied, on 1st floor, doors shut, 'to-2nd' button)

DOWN_incar = A . C . H . F (occupied, on 2nd floor, doors shut, 'to-1st' button)

Final results — Question 7
Output	Boolean expression
$UP$ (corridor call, part a)	$B\cdot E\cdot H\cdot A'$
$UP_{incar}$ (part b)	$A\cdot B\cdot H\cdot G$
$DOWN_{incar}$ (part b)	$A\cdot C\cdot H\cdot F$

Topic: Combinational logic design from a word specification.

Key relations: each output is a product (AND) of the sensor literals that must all be true simultaneously; a "disabled unless condition X" requirement becomes an extra AND'd literal ($X$ or $X'$) rather than a separate gate stage.

Why this works: because "at most one sensor changes at a time" and every rule in the spec is a simple conjunction of conditions, no simplification (Karnaugh map, don't-cares) is needed beyond directly conjuncting the literals the word problem names — the specification is already in minimal sum-of-one-product form for each output.

Common pitfall: forgetting to gate the corridor call with $A'$ (or the in-car button with $A$) — omitting either disable condition would let a corridor button move an occupied car or an in-car button move an empty one, violating the stated safety rules.

Source: Mano, Digital Design, Ch. 2–3 (Boolean algebra, combinational logic design).

Question 7 of 7: Combinational Logic — Two-Floor Elevator Control

Question 7: Combinational Logic — Two-Floor Elevator Control (20 marks)