{"id":714,"date":"2013-06-29T00:40:00","date_gmt":"2013-06-29T00:40:00","guid":{"rendered":"http:\/\/www.themissingdocs.net\/wordpress\/?p=714"},"modified":"2013-06-29T00:40:00","modified_gmt":"2013-06-29T00:40:00","slug":"binary-functions","status":"publish","type":"post","link":"https:\/\/www.themissingdocs.net\/?p=714","title":{"rendered":"Binary Functions"},"content":{"rendered":"

There are 16 binary functions over 2 variables.\u00a0 This is a simple consequence of there being 4 input possibilities and only 2 output possibilities for each.\u00a0 In computer programming we frequently use ‘and’ and ‘or’, less often ‘xor’, but that still leaves 13 more.<\/p>\n

Lets take a closer look at all 16.\u00a0 For brevity I will label each by their outputs for the inputs F,F T,F F,T T,T – so ‘and’ is FFFT.<\/p>\n

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  1. TTTT – ‘always true’.\u00a0 Not very interesting, but it exists.<\/li>\n
  2. FFFF – ‘always false’.\u00a0 Again not very interesting.<\/li>\n
  3. FFFT – ‘and’.\u00a0 Well known and used in programming frequently.<\/li>\n
  4. TTTF – ‘not and’.\u00a0 Simple combination of the negation function with the and.<\/li>\n
  5. FTTT – ‘or’.\u00a0 Well known and used in programming frequently.<\/li>\n
  6. TFFF – ‘not or’.\u00a0 Simple combination of negation and ‘or’.<\/li>\n
  7. FTTF – ‘xor’.\u00a0 Not quite as well known as ‘or’, but simply ‘or’ where it can’t be both.<\/li>\n
  8. TFFT – ‘not xor’.\u00a0 Again a simple combination of negation and ‘xor’.\u00a0 But it is also the A == B scenario and thus xor can also be described as A != B.<\/li>\n
  9. FFTT – ‘B is true’.\u00a0 First parameter is ignored, and second is just passed through.<\/li>\n
  10. TTFF – ‘B is not true’.\u00a0 Again just the negation of the one before.<\/li>\n
  11. FTFT – ‘A is true’.\u00a0 This time the second parameter is ignored.<\/li>\n
  12. TFTF – ‘A is not true’.\u00a0 Yet another simple negation.<\/li>\n
  13. TFTT – ‘A implies B’.\u00a0 If A is true, B must be true, but otherwise anything goes.<\/li>\n
  14. FTFF – ‘A and (not B)’.\u00a0 This is also the negation of ‘A implies B’ but programming sees combinations of ‘and’ and ‘not’ far more frequently.<\/li>\n
  15. TTFT – ‘B implies A’.\u00a0 If B is true, A must be true.<\/li>\n
  16. FFTF – ‘(not A) and B’.\u00a0 As for 14, but reversed.<\/li>\n<\/ol>\n

    So, why did I list all these?\u00a0 So I could categorize them.<\/p>\n