welcome to digital electronics lecture series i professor it is Dholakia is going to explain you six variable k-map in this session so to understand six variable k-map first I will give you problem and then we will solve it step by step so here question is so here we have six variable k-map and we are a little bit to solve this six variable function by boolean expression using six variable k-map so here first if you observe there are total six variable so n is equals to 6 and as per that total cells that we can say that is 2 to the power n that is 2 to the power 6 means 64 so as if you have 64 cells all we can do is we can take this to a be to identify these variables as a 16 cells group so for example if I say we have a B that is 0 0 for example if I say we have a B that is 1 z 0 1 if I say a B that is 1 0 over here and a B that is 1 1 then I can have by section of this function in 16 group with four different groups right so here all we will be doing is we will bisect this ABCDE F based on 16 group cell where c d e f structure will be as per 16 cells Karnad map right so let me draw 16 cell karnaugh map first so here you can see c d e f is there so c d e f that is having C D which is 0 0 0 1 1 1 1 0 EF will be 0 0 0 1 1 1 1 0 that is how it is there and similarly this will be there with a B 1 0 a B 0 1 a B 1 1 alright so now you can clearly observe see what I have done is I have bisected a b c d e f into a b and c d e f where a b is 0 0 0 1 1 0 and 1 1 like this and c d e f that is as per 16 cells k map right that is how I have bisected now first if you want to identify what will be the locations then see a B is 0 0 and c d e f 0 0 so it will start from 0 from over here and then 1 2 3 4 5 6 7 8 9 10 sorry 10 11 then 12 13 14 and 15 that is how it is increasing after that a B is 0-1 so next 16 will be over here right and then 17 18 19 20 21 22 23 24 25 26 27 28 29 30 and 31 see that is how it is there after that a B is 1 0 so 32 will start from here so 32 33 34 35 36 37 38 39 then you see I need to jump this column 40 41 42 43 44 45 46 and 47 after that a B is 1 1 so 48 will starts from here 48 49 50 51 52 53 54 55 then 56 57 58 59 and 60 61 62 and 63 see this is how total 64 cells will be there right now all I need to do is I need to identify what are the locations of ones so it is there at 0 5 7 so 0 then 5 then 7 then 8 then 9 then 12 then 13 then 23 so 23 I am just speaking you can listen 23 means over here twenty four twenty five twenty eight twenty nine thirty seven so 37 that is there in this so again 37 means over here then 40 42 44 46 and then 55 so I need to go in this 55 then 56 then 57 then 60 and 61 alright so that is how locations are there you can clearly observe it right now here we need to form a groups right now we need to form a groups and we need to form a group which is largest one right and try to understand this you can see C grouping can be done as per this direction like this two can be combined these two can be combined these two can be combined and this two we can combine right to form a largest group see this is how it is there now if you op so first see this 4 and this 4 can be combined together right this 4 and this 4 that we can combined together and that will form 8 cells group so I am combining this 4 and this 4 which is forming 8 cells group so this is my first group right and in this first group you can observe a B is 0 1 and 1 1 so B is 1 which is common is changing right so I can say this is a group which is B right after that we need to see in this as this is same right so here if you observe CD that is 1 1 1 0 so C is 1 d is changing and in this EF is 0 0 1 0 1 so E is bad so we see EEMA this is my first group right now I need to see any other group which is possible with largest combination see this 4 can form a group this 4 and this 4 can combine on each other right this 4 and this 4 that can combine on each other so you can observe this 4 and this 4 that is my second group and that second group is having a B 0 0 and a B 0 1 means first later is common which is a is 0 means a bar now in this we can see C D that is 1 1 1 0 so C is 1 and e F that is 0 0 0 1 so E is 0 so e bar so second group covers this 8 cells right now I need to see what is largest group over here right so for that I see this is a group which is forming for cell group right so this is my third group for cell group and that group is having a B that is 1 0 means a B bar right and if you observe C D so that is 1 1 1 0 so C is 1 D is changing and if you observe here so that is 0 0 and 1 0 so f is bar over here so that is how I have third group now I need to see what are other possibilities so now you can observe over here C to have a formation of next group you can see see this one and this one is forming on each other so we can take this as a common group so this is my fourth group now in this fourth group if you observe a B is 0 1 and 1 1 so B is common so B is 1 so me and then C D that is 0 1 means C bar D and E F is 1 1 so e F so that is my fourth group so now this is covered completely now I need to cover this right so over here you can see this and this is getting combined so this is my fifth group now in this fifth group you can see a B is zero zero one zero so it is B bar as a is changing and C D is 0 1 so that is C bar D and E F is 0 1 so that is e bar F now I just need this one and this one so this one that I can simply make by this combination right so to sell combination I can have even this and this combination but I'm making this combination so this is my sixth group and that is maybe zero zero so a bar b bar and then CD that is 0 1 so C bar d and e F is 0 1 and 1 1 so f is 1 so this is 6 the group and only this one is required to be covered so I can say this and this sell so that is 7th group and that 7th is having a B that is 0 0 so a bar b bar and then you can see CD that is 0 0 1 0 so the is common so d bar and you can see EF is 0 0 so e bar f bar so that is how total seven group are there and now it covers all one's in this question right it covers all one's in this question so now I need to write this answer so start from first group right so that is BC e bar plus second group so that is a bar C Y bar plus third group that is a B Bar C F bar plus fourth group that is e C bar d e f plus v group that is B Bar C bar de f +6 group that is a bar b Bar C bar DF plus seven group that is a bar b bar d bar y bar f bar so this is how we can resolve boolean expression right by having six variable k-map so this is what we need to focus about this is the basic process you should follow here I'm explaining you otherwise when you solve it by yourself you will be finding this is bit faster than this right so just follow the practice way that I am explaining and then you will be finding this is easier one right I hope that you will be under you are understanding all those things which I am teaching here please give your valuable feedback the reason is your free robux only encouraging me and that is highly required to me thank you so much for watching this video