I have attached an image of a k-map of 5 variables ABCDE that I have. I don't understand why the implicants circled in red or green are is an essential implicant? According to my understand of grouping in K-map, all 1s must be circled. So wouldn't either the red or green circled region one of the essential implicants so that cell no. 7 will be covered? Thanks.
If I could remember correctly. If a minterm(square) is covered by only one prime implicant then that implicant is called essential prime implicant. Therefore in your map there are 3 essential prime implicants (1,16) because only this covers both 1 and 16 (5,21) because only this covers 21 (6,14,22,30) because only this covers 14, 22 and 30 Only the minterm 7 is left out. Since 7 can be covered by either (5,7)(red in your figure) or (6,7)(green) both are not essential prime inplicants. Any one of the 2 can be used to complete the map.
Thanks for replying. So do I omit both the red and green circled implicants or do I include either one of it into my final result? If I have to omit them, why isn't either the red or green circled implicants an essential prime implicants when minterm 7 is not even covered by a prime implicant yet?
You have to include either one of them(I have clearly explained it in my previous post). Read my definition again. Since 7 is covered by both. both are not essential. Let me give an example. You need water to survive hence its essential(nothing else can substitute it). You need food but that can be either fruits or vegetables or something else. So fruits and vegetables cannot be considered as essential. Sometimes even bread will do.
ahhh...thanks!! haha...nice analogy! I get what you mean now. I kept thinking that the final sum of minterms consist of only essential prime implicants. So looks like my final result can consist of non-essential prime implicants BUT must be at least of prime implicants. If this is the case, what is the purpose of essential prime implicants since the prime implicants is enough to get the final result?
You still didnt get it it seems. Without essential prime implicants you cannot get a solution. sometimes essential prime implicants are enough to get a solution. in some cases other prime implicants are needed to complete the solution. thats the main reason why they named it as essenial. Essential have no substitutes. they must always be included in the solution but other primeimplicants have substitutes. hope you got it.
ok, I think I see some connection now. The essential prime implicants are the sets of regions that MUST be added into the final results. There may be other prime implicants that could cover the essential prime implicant regions but we will just ignore those since the essential prime implicants are usually the largest region that it could cover. Therefore, they are considered the essentials. There are however some areas not covered by the essential prime implicants. These areas are covered by several prime implicants that can be replaced by one another to have the same area covered. So they are not the essentials one though either one of the possible prime implicants need to be added into the final result so that all the minterms are covered. thanks a lot!!