Video instructions and help with filling out and completing When Form 5495 Minimizing

Instructions and Help about When Form 5495 Minimizing

Ha ha ha you you in the last lecture we introduced you to the map method of boolean simplification we do a karnaugh map which is a graphical representation of a truth table filled this graph it once correspond to the cells for which whose midterms had a output true and zeroes of course we didn't mark zeros to avoid cluttering at the map wherever we did not mark a1 in the map the end device is 0 which is purposely left out so that the map doesn't get cluttered we the object is to identify groups of ones as large as possible of course with the satisfying the adjacency rule and remove or knock off as many variables as possible so that by repeatedly doing this we can get a simpler representation of a given boolean function so we look at a few more examples today some special cases and all that I will take an example of a map like this four variables we call this variable the ABCD Pradas alias web has once in the following cells is the Battle of once that means this is a function which is X plus the sum of the following min terms this is min term number two so you got started from here 0 1 2 3 2 4 5 6 7 8 9 10 11 12 13 14 15 right this is the map now the idea is to group adjacent ones with as large groups as possible keeping in mind the group should be as large as possible if we have a smaller group which can be totally submerged in the larger group we should not consider the smaller group and we have to make sure that all ones are covered and we do not mind a 1 being covered more than once these are the rules make as large groups as possible keeping in mind that just since it all the extras are all ones are covered do not worry about combining more than one a given one more than once and so there are only two groups of 1 some groups of 2 only in this part in this map only groups of two are paths groups of 2 ones are only possible 1 2 3 4 so this is I can say this because this one has to be covered anyway this is standing out separately the most efficient way would probably be not covering anything more than once is the most efficient way right as long as you can cover one more than once if it can result in a smaller group if something is not going to result in a smaller group there's no point in covering a 1 more than once so in this case there only 2 ones this is going to be a group this is going to be group there is going to be group all groups are having two ones so there is no point in unnecessarily doing this and doing this so this is what I would do some I will write this three one three groups of two ones eh and what this what would this be in terms of the variable in terms of the expression product expression so f would be some of these products 1 2 3 this would be a C bar D then this will be b c d this would be a bar C D bar now instead of doing this way suppose I marked it slightly differently let me rewrite here suppose I put like this suppose it's obviously not the most efficient way you can see that because it's a small mayor the small map with a few ones but in general only have a large map with large possible groups you may miss out and may do things like this I brought this up to explain some of the definitions we gave in the last lecture I talked about implicant the prime implicant and an essential prime implicant implicant is any group of ones is called an implicant a prime implicant is the largest possible group of ones in the given group of course that cannot be in a sense l prime implicant a prime implicant is a group which cannot become part of another implicant an essential prime implicant is one which I said if you remember has at least one entry of one not covered in any other prime implicant so this way here this is the residential prime implicant we'll call this 1 2 3 this is 1 1 is an essential prime implicant because this one cannot be covered otherwise 3 is an essential prime 2 can be gas these cannot be covered otherwise no is to an essential problem is to an essential prime implicant or not is the question do you think too is an essential prime implicant or not the way I draw it it is an essential for American because this one these two one cannot be covered in email but if when I draw this map there are two ways of combining these two ones this is an essential prime implicant this is an essential prime implicant is this a prime implicant what is a prime implicant the largest group of one's possible within that this is a largest possible group of one's so all the 4 here I will call this 1 2 3 4 here all the four are prime implicants here all the 3 are prime implicants but one and three are clearly essential prime implicant 2 is not an essential prime implicant it's a non essential prime implicant for the simple reason I can cover these two ones in two other ways so in this case again what is an essential prime implicant for instance o2 is a non epi for the reason that this one could have been combined with this I could have made a small it's an essential prime