[Geek] Binary Operators
Just an entry about the way binary operators work so I can later discuss trinary.
Unary Operators: Input 01 OutputAlways 000 No Change01 Not10 Always 111Of the possible unary operations NOT is the only one that actually does something. The other three either ignore the input, or don't modify the input at all.
Binary Operators: Input - A B 0 00 11 01 1 OutputAlways 00000 A And B0001 A And (Not B)0010 A0011 (Not A) And B0100 B0101 A Xor B0110 A Or B0111 Not (A Or B)1000 Not (A Xor B)1001 Not B1010 A Or (Not B)1011 Not A1100 (Not A) Or B1101 Not (A And B)1110 Always 11111 There are 16 possible binary operations. Six of these operations ignore one or both inputs. By applying NOT to either the inputs or the output you can transform some operators into other operators, leaving only three operator groups: And, Or, and Exclusive Or (a.k.a. Xor). NOT could be applied more than once to allow more than one way to "get to" the other operators, but we still need the three operators to get to them all.
Unary Operators: Input 01 OutputAlways 000 No Change01 Not10 Always 111Of the possible unary operations NOT is the only one that actually does something. The other three either ignore the input, or don't modify the input at all.
Binary Operators: Input - A B 0 00 11 01 1 OutputAlways 00000 A And B0001 A And (Not B)0010 A0011 (Not A) And B0100 B0101 A Xor B0110 A Or B0111 Not (A Or B)1000 Not (A Xor B)1001 Not B1010 A Or (Not B)1011 Not A1100 (Not A) Or B1101 Not (A And B)1110 Always 11111 There are 16 possible binary operations. Six of these operations ignore one or both inputs. By applying NOT to either the inputs or the output you can transform some operators into other operators, leaving only three operator groups: And, Or, and Exclusive Or (a.k.a. Xor). NOT could be applied more than once to allow more than one way to "get to" the other operators, but we still need the three operators to get to them all.