Question

A gold vault has 3 locks with a key for each lock. Key A is owned by the

manager whilst Key B and C are in the custody of the senior bank teller

and the trainee bank teller respectively. In order to open the vault door at

least two people must insert their keys into the assigned locks at the same

time. The trainee bank teller can only open the vault when the bank

manager is present in the opening.

i) Determine the truth table for such a digital locking system (4 marks)

ii) Derive and minimize the SOP expression for the digital locking system
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Answer 1

• see the attached truth table
• Opens = AB + AC

Step-by-step explanation:

i) In the attached truth table, TRUE means the respective key owner is present and their keys are inserted at the same time. The "Opens" column is TRUE when two owners are present, not including the case where the only two owners present are B and C.

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ii) The second attachment is a Karnaugh map of the truth table. The circled terms are ...

Opens = AB +AC