441
edits
Anisomorphism
Joined 24 January 2021
→Gates
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XOR is only "true" or 1 when x or y but not both, are 1. Disjunctive normal form says that we can view the x, y entries as unary operators which return the input with no change, combine these as given on the lines which evaluate to 1, and take the OR of all of them for the total connective form of the truth table. Here is the second line: <math> x\and\neg y</math>. The total is:<math> (x\and\neg y)\or (\neg x\and y)</math>, which can be viewed as a sum of "elementary functions" which are only 1 on one line, and building a general function/table that way. | XOR is only "true" or 1 when x or y but not both, are 1. Disjunctive normal form says that we can view the x, y entries as unary operators which return the input with no change, combine these as given on the lines which evaluate to 1, and take the OR of all of them for the total connective form of the truth table. Here is the second line: <math> x\and\neg y</math>. The total is:<math> (x\and\neg y)\or (\neg x\and y)=(x\or(\neg x\and y))\and(\neg y(\neg x\and y))</math>, which can be viewed as a sum of "elementary functions" which are only 1 on one line, and building a general function/table that way. | ||
= Read prototype = | = Read prototype = | ||