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→Step 1: finding prime implicants: more clarification |
m →Example: formatting |
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This expression says that the output function f will be 1 for the minterms <math>4,8,10,11,12</math> and <math>15</math> (denoted by the 'm' term) and that we don't care about the output for <math>9</math> and <math>14</math> combinations (denoted by the 'd' term). The summation symbol <math>\sum</math> denotes the logical sum (logical OR, or disjunction) of all the terms being summed over.
===Step 1:
First, we write the function as a table (where 'x' stands for don't care):
:{| class="wikitable"
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Note: In this example, none of the terms in the size 4 implicants table can be combined any further. In general, this process is continued in sizes that are powers of 2 (sizes 8, 16 etc.) until no more terms can be combined.
===Step 2:
None of the terms can be combined any further than this, so at this point we construct an essential prime implicant table. Along the side goes the prime implicants that have just been generated (these are the ones that have been marked with a "{{color|red|*}}" in the previous step), and along the top go the minterms specified earlier. The don't care terms are not placed on top—they are omitted from this section because they are not necessary inputs.
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