Boolean Logic and Logic Gates: Question 4
Syllabus 10.1, 10.2, 10.3
At the GameOn Arena esports tournament, a check-in kiosk decides whether to unlock a turnstile using output Access, based on three inputs:
- Q = 1 when the player's QR-code ticket scans as valid, 0 otherwise
- D = 1 when the kiosk's camera confirms the player's face matches their photo ID, 0 otherwise
- K = 1 when a staff member inserts a physical override key, 0 otherwise
The turnstile unlocks according to the logic expression: Access = (Q AND D) OR K
(a) State the name of the single logic gate that combines Q and D, before the result is combined with K. [1]
(b) Complete the truth table for Access, showing all eight combinations of Q, D and K. [4]
| Q | D | K | Access |
|---|---|---|---|
| 0 | 0 | 0 | |
| 0 | 0 | 1 | |
| 0 | 1 | 0 | |
| 0 | 1 | 1 | |
| 1 | 0 | 0 | |
| 1 | 0 | 1 | |
| 1 | 1 | 0 | |
| 1 | 1 | 1 |
(c) A tournament organiser says the override key should only ever act as a backup, and must never by itself be the sole reason a player is let in. Using your completed truth table, explain whether the current design meets this requirement. [2]
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Worked solution
Part (a): Naming the first gate
Q and D must both be 1 before their combined result is fed onward, since the expression groups them as (Q AND D). A gate whose output is 1 only when both inputs are 1 is an AND gate.
Part (b): Building the truth table row by row
First evaluate Q AND D, then combine that result with K using OR, since Access = (Q AND D) OR K.
| Q | D | K | Q AND D | Access = (Q AND D) OR K |
|---|---|---|---|---|
| 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 1 |
| 0 | 1 | 0 | 0 | 0 |
| 0 | 1 | 1 | 0 | 1 |
| 1 | 0 | 0 | 0 | 0 |
| 1 | 0 | 1 | 0 | 1 |
| 1 | 1 | 0 | 1 | 1 |
| 1 | 1 | 1 | 1 | 1 |
Whenever Q and D are not both 1, Q AND D = 0, so Access simply follows K (OR with 0 leaves the other value unchanged): Access = 0 if K = 0, and Access = 1 if K = 1. Whenever Q and D are both 1, Q AND D = 1, and OR with anything gives 1, so Access = 1 regardless of K.
So the completed table for Access is:
| Q | D | K | Access |
|---|---|---|---|
| 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 1 |
| 0 | 1 | 0 | 0 |
| 0 | 1 | 1 | 1 |
| 1 | 0 | 0 | 0 |
| 1 | 0 | 1 | 1 |
| 1 | 1 | 0 | 1 |
| 1 | 1 | 1 | 1 |
Part (c): Checking the organiser’s requirement
The organiser wants the key to be a backup only, never the sole reason for entry. Look at the row where Q = 0, D = 0 and K = 1: neither the ticket nor the photo check has passed, yet Access = 1 because K = 1 makes the OR true on its own.
This means the current design does not meet the requirement: a staff member can let a player through using only the override key, with no valid ticket and no ID match at all, which is more than “backup” behaviour.
Final answers
- (a) AND gate
- (b) Access values in row order: 0, 1, 0, 1, 0, 1, 1, 1
- (c) No. The design does not meet the requirement, because row (Q = 0, D = 0, K = 1) gives Access = 1, so the override key alone can unlock the turnstile.