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in Digital Logic by Active (2.3k points) | 293 views
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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.
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In ques it is mentioned that all the keys are not inserted at the same time so why we have taken abc as 1.
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Oh yes..you are correct :) But then also answer will be same right?
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Then i am not getting ans as 6
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Can you please show your Circuit?

I got 6 so didn't try to minimize it :P
+1
Expression will be ABC`+ AB'C+A'BC so how to realized i using 2 input nand gates
+1

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

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

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Okkkkk
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 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 -  $ABC`+ AB'C+A'BC$

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I am also confused....

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