4/23/2021 0 Comments Methode De Quine-Mc Cluskey
It can be shown that for a function of n variables the upper bound on the number of prime implicants is 3 n n.But it also says that we dont care about the output for 9 and 14 combinations (denoted by the d term).So to optimize, all minterms that evaluate to one are first placed in a minterm table.Dont-care terms are also added into this table, so they can be combined with minterms.
Terms that cant be combined any more are marked with an asterisk (). When going from Size 2 to Size 4, treat - as a third bit value. ![]() Be aware that this processing should be continued otherwise (size 8 etc.). Along the side goes the prime implicants that have just been generated, and along the top go the minterms specified earlier. The dont care terms are not placed on top - they are omitted from this section because they are not necessary inputs. If a column has only 1 X, this means that the minterm can only be covered by 1 prime implicant. Minterm 15 also has only 1 X, so m(10,11,14,15) is also essential. If a prime implicant is essential then, as would be expected, it is necessary to include it in the minimized boolean equation. In some cases, the essential prime implicants do not cover all minterms, in which case additional procedures for chart reduction can be employed. Methode De Quine-Mc Cluskey Trial And ErrorThe simplest additional procedure is trial and error, but a more systematic way is Petricks Method. In the current example, the essential prime implicants do not handle all of the minterms, so, in this case, one can combine the essential implicants with one of the two non-essential ones to yield one equation. The American Mathematical Monthly. Retrieved 25 August 2014. Bell System Technical Journal. Retrieved 24 August 2014. The R implementation is exhaustive and it offers complete and exact solutions.
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