![]() ![]() None of the terms can be combined any further than this, so at this point we construct an essential prime implicant table. In general this process should be continued (sizes 8, 16 etc.) until no more terms can be combined. Note: In this example, none of the terms in the size 4 implicants table can be combined any further. 110 corresponds to BCD' whileĠ11- corresponds to A'BC, and BCD' + A'BC is not equivalent to a product term. For instance, -110 and -100 can be combined to give -1-0, as can -110 and -010 to give -10, but -110 and 011- cannot since the -'s do not align. So to match two terms the -'s must align and all but one of the other digits must be the same. ![]() The remaining variables present should agree. One of the variables should be complemented in one term and uncomplemented in the other. The terms represent products and to combine two product terms they must have the same variables. When going from Size 2 to Size 4, treat - as a third bit value. For instance 10 can be combined to give 100-, indicating that both minterms imply the first digit is 1 and the next two are 0. Terms that can't be combined any more are marked with an asterisk ( *). If two terms differ by only a single digit, that digit can be replaced with a dash indicating that the digit doesn't matter. ![]() Don't-care terms are also added into this table (names in parentheses), so they can be combined with minterms:Īt this point, one can start combining minterms with other minterms. So to optimize, all minterms that evaluate to one are first placed in a minterm table. One can easily form the canonical sum of products expression from this table, simply by summing the minterms (leaving out don't-care terms) where the function evaluates to one:į A,B,C,D = A'BC'D' + AB'C'D' + AB'CD' + AB'CD + ABC'D' + ABCD. Step 1: finding prime implicants įirst, we write the function as a table (where 'x' stands for don't care): the subset S = denotes the logical sum (logical OR, or disjunction) of all the terms being summed over. Hasse diagram of the search graph of the algorithm for 3 variables. ![]()
0 Comments
Leave a Reply. |