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A student from the Electronics department is asked to design a digital alarm for a smart home…
A student from the Electronics department is asked to design a digital alarm for a smart home security system for the outside area. It comprises a sensor and a digital identification (ID) card with six-digit personal identification number (PIN). The alarm is supposed to buzz if wrongful entry is attempted, either by breaking the glass window or by entering the wrong PIN.
Following statements are the criteria for the alarm to buzz:
• The sensor detects the door opening without scanning a digital ID card.
or
• The sensor detects the door opening by breaking of the door lock.
or
• The sensor detects the wrong pin entry thrice of the digital ID card while opening the door.
The inputs are:
(In all the above cases 1 indicates Yes and 0 indicates No).
Output: A – Denotes the buzz of security alarm system (1 indicates yes and 0 indicates no)
Draw the truth table for the inputs and outputs given above. Write the canonical POS expression for A(D, B, S, P).
| Inputs | Description |
|---|---|
| D | Door opening |
| B | Breaking of door lock |
| S | Scanning security card |
| P | Entering correct six-digit pin less than three times |
Answer
Answer
AITruth table (D B S P -> A), verified with the boolean tool:
(A=1 whenever the door opens without scanning the card (D=1,S=0), or the lock is broken (D=1,B=1), or the door opens after the wrong pin is entered 3 times (D=1,P=0); reasoned as A = D.S' + D.B + D.P'.)
Canonical POS (from the 0-rows, maxterms 0,1,2,3,7,8,9,10,11):
$A(D,B,S,P) = (D+B+S+P)(D+B+S+P')(D+B+S'+P)(D+B+S'+P')(D+B'+S'+P')(D'+B+S+P)(D'+B+S+P')(D'+B+S'+P)(D'+B+S'+P')$
| D | B | S | P | A |
| 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 1 | 1 | 0 |
| 0 | 1 | 0 | 0 | 1 |
| 0 | 1 | 0 | 1 | 1 |
| 0 | 1 | 1 | 0 | 1 |
| 0 | 1 | 1 | 1 | 0 |
| 1 | 0 | 0 | 0 | 0 |
| 1 | 0 | 0 | 1 | 0 |
| 1 | 0 | 1 | 0 | 0 |
| 1 | 0 | 1 | 1 | 0 |
| 1 | 1 | 0 | 0 | 1 |
| 1 | 1 | 0 | 1 | 1 |
| 1 | 1 | 1 | 0 | 1 |
| 1 | 1 | 1 | 1 | 1 |
From ISC Computer Science - Competency Focused Practice Questions (CISCE, August 2024), question 67.
Check your working with the Boolean algebra solver: the steps law by law, the K-map and the logic circuit for any expression.