1 votes 1 votes Caption Priyanka Agarwal asked Jul 21, 2018 Priyanka Agarwal 1.4k views answer comment Share Follow See all 14 Comments See all 14 14 Comments reply MiNiPanda commented Jul 21, 2018 reply Follow Share 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. 0 votes 0 votes Priyanka Agarwal commented Jul 21, 2018 reply Follow Share In ques it is mentioned that all the keys are not inserted at the same time so why we have taken abc as 1. 0 votes 0 votes MiNiPanda commented Jul 21, 2018 reply Follow Share Oh yes..you are correct :) But then also answer will be same right? 0 votes 0 votes Priyanka Agarwal commented Jul 21, 2018 reply Follow Share Then i am not getting ans as 6 0 votes 0 votes MiNiPanda commented Jul 21, 2018 reply Follow Share Can you please show your Circuit? I got 6 so didn't try to minimize it :P 0 votes 0 votes Priyanka Agarwal commented Jul 22, 2018 reply Follow Share Expression will be ABC`+ AB'C+A'BC so how to realized i using 2 input nand gates 1 votes 1 votes MiNiPanda commented Jul 22, 2018 reply Follow Share 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 1 votes 1 votes Soumya29 commented Jul 22, 2018 reply Follow Share $Expression - AB +BC + CA$ And $6 \ NAND$ gates are required. $AB +BC + CA$ can be written as $\overline {\overline {(AB +BC)}. \overline {(CA)}}.$ 0 votes 0 votes Priyanka Agarwal commented Jul 22, 2018 reply Follow Share Which product terms you have taken as 1 0 votes 0 votes Priyanka Agarwal commented Jul 22, 2018 reply Follow Share To open all the locks simultaneously we have to insert all the simultaneously 0 votes 0 votes Soumya29 commented Jul 22, 2018 reply Follow Share "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. 0 votes 0 votes Priyanka Agarwal commented Jul 22, 2018 reply Follow Share Okkkkk 0 votes 0 votes Soumya29 commented Jul 22, 2018 reply Follow Share 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 - $ABC`+ AB'C+A'BC$ 0 votes 0 votes Priyanka Agarwal commented Jul 22, 2018 reply Follow Share I am also confused.... 0 votes 0 votes Please log in or register to add a comment.