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in Digital Logic by Active (2.3k points) | 293 views
Let A, B and C be the 3 keys owned by 3 different persons. If atleast two of them can open the lock then the vault will open.

If A opens the lock then I say A=1 else A=0.

So now according to the condition given, AB+BC+CA+ABC=1 i.e. if any two or all 3 open the lock then vault opens.

Hence, AB=1, BC=2,CA=1 and ABC=1. After minimizing we get AB+BC+AC=1.

If realized using Nand gates we get 6.
In ques it is mentioned that all the keys are not inserted at the same time so why we have taken abc as 1.
Oh are correct :) But then also answer will be same right?
Then i am not getting ans as 6
Can you please show your Circuit?

I got 6 so didn't try to minimize it :P
Expression will be ABC`+ AB'C+A'BC so how to realized i using 2 input nand gates

i am getting a confusion here... the Q says that

"to open a vault at least two people must insert their keys..."

What is the significance of "at least" here if we take exactly 2 people opening the locks?

Also it reads that

All the keys are not inserted at the same time...

Initially i thought it meant that a Gate cannot have more than 2 i/p terminals. It does not say that "All the locks cannot be OPENED at the same time". If it was given so then ABC'+ACB'+BCA'=1 would have been correct.

Correct me if i'm wrong

$Expression - AB +BC + CA$
And $6 \ NAND$ gates are required.
 $AB +BC + CA$ can be written as $\overline {\overline {(AB +BC)}. \overline {(CA)}}.$
Which product terms you have taken as 1
To open all the locks simultaneously we have to insert all the  simultaneously

"to open a vault at least two people must insert their keys..."

This line tells that $atleast  \ 2 $ of the  $3$ keys are required to open the vault. Presence of $3^{rd}$ key doesn't matter.
So 6 minterms are there in the expression-
After minimization, we get $AB+BC+CA$

All the keys are not inserted at the same time...

This line is there just to confuse us. 


 Still, I am confused a bit. If we consider these 2 lines simultaneously -

"To open a vault at least two people must insert their keys...
All the keys are not inserted at the same time..."

then it means that EXACTLY 2 keys are required.
And then Expression would be -  $ABC`+ AB'C+A'BC$

I am also confused....

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