What are XAND and XOR

Question

What are XAND and XOR  Also is there an XNot

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There is no such thing as Xand or Xnot   There is Nand  which is the opposite of and  TRUE and TRUE     TRUE TRUE and FALSE    FALSE FALSE and TRUE    FALSE FALSE and FALSE   FALSE   TRUE nand TRUE     FALSE TRUE nand FALSE    TRUE FALSE nand TRUE    TRUE FALSE nand FALSE   TRUE

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OMG  a XAND gate does exist  My dad is taking a technological class for a job and there IS an XAND gate  People are saying that both OR and AND are complete opposites  so they expand that to the exclusive-gate logic   XOR  One or another  but not both  Xand  One and another  but not both   This is incorrect  If you re going to change from XOR to XAND  you have to flip every instance of  AND  and  OR    XOR  One or another  but not both  XAND  One and another  but not one   So  XAND is true when and only when both inputs are equal  either if the inputs are 0 0 or 1 1

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There s a simple argument to see where the binary logic gates come from  using truth tables  which have come up already   There are six that represent commutative operations  in which a op b    b op a  Each binary operator has an associated three column truth table that defines it  The first two columns can be fixed for the defining tables for all the operators   Consider the third column  It s a sequence of four binary digits  There are sixteen combinations  but the constraint of commutativity effectively removes one row from the truth tables  so it s only eight  Two more get knocked off because all truths or all falses isn t a useful gate  These are the familiar or  and  and xor  plus their negations

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XOR is Exclusive Or   It means  One of the two items being XOR d is true  but not both of them    TRUE XOR TRUE   FALSE TRUE XOR FALSE   TRUE FALSE XOR TRUE   TRUE FALSE XOR FALSE  FALSE   Wikipedia s XOR Article  XAND I have not heard of

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XOR  not neither and not both  B 0110  is the inverse  dual  of IFF  if and only if  B 1001

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This is what you are looking for  https   en wikipedia org wiki XNOR gate  Here is the logic table   A B   XOR XNOR 0 0   0   1  0 1   1   0 1 0   1   0 1 1   0   1   XNOR sometimes is called XAND

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XOR behaves like Austin explained  as an exclusive OR  either A or B but not both and neither yields false   There are 16 possible logical operators for two inputs since the truth table consists of 4 combinations there are 16 possible ways to arrange two boolean parameters and the corresponding output   They all have names according to this wikipedia article

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The truth tables on Wiki clarify http   en wikipedia org wiki Logic gate There is no XAND  and that is the end of part 1 of the questions legitimacy   The point is you can always make do without it    I personally have mistaken XNOT  which also doesn t exist  for NAND and NOR which are theoretically the only thing you need to make all the other gates link  I believe the confusion stems from the fact that you can use either NAND or NOR  to create everything else  but they are not needed together    so it s thought of as one thing that s both NAND and NOR together  which basically leaves the mind to supplant the remaining name XNOT which isn t used so it s what I wrongly call XNOT meaning it s either NAND or NOR   I suppose one could also wrongly in quick discussion try to use the XAND like I do XNOT  to refer to the  a single gate  copied in various arrangements  makes all other gates  logical reality

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Hmm   well I know about XOR  exclusive or  and NAND  and NOR   These are logic gates and have their software analogs   Essentially they behave like so   XOR is true only when one of the two arguments is true  but not both   F XOR F   F F XOR T   T T XOR F   T T XOR T   F   NAND is true as long as both arguments are not true   F NAND F   T F NAND T   T T NAND F   T T NAND T   F   NOR is true only when neither argument is true   F NOR F   T F NOR T   F T NOR F   F T NOR T   F

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In the book written by Charles Petzold titled  Code  he says there are 6 gates  There is the AND logical gate  the OR gate  the NOR gate  the NAND gate  and the XOR gate  He also mentions the 6th gate briefly calling it the  coincidence gate  and implies it s not used very often  He says it has the opposite output of a XOR gate because a XOR gate has the output of  false  when it has two true or two false sides of the equation and the only way for a XOR gate to have its output be true is for one of the sides of the equation to be true and the other to be false  it doesn t matter which  The coincidence is the exact opposite of this because with the coincidence gate if one is true and the other is false  doesn t matter which is which  then it will have its output be  false  in both those cases  And the way for a coincidence gate to have its output be  true  is for both sides to be either false or true  If both are false the coincidence gate will evaluate as true  If both are true then the coincidence gate will also output  true  in that case as well   So in the cases where the XOR gate outputs  false   the coincidence gate will output  true   And in the cases where the XOR gate will output  true   the coincidence gate will output  false

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XOR is short for exclusive or   It is a logical  binary operator that requires that one of the two operands be true but not both   So these statements are true   TRUE XOR FALSE FALSE XOR TRUE   And these statements are false   FALSE XOR FALSE TRUE XOR TRUE   There really isn t such a thing as an exclusive and   or XAND  since in theory it would have the same exact requirements as XOR   There also isn t an XNOT since NOT is a unary operator that negates its single operand  basically it just flips a boolean value to its opposite  and as such it cannot support any notion of exclusivity

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Have a look  x   y      A    B   C   D   E   F   G   H   I   J   K   L   M   N               T         T        T        T        T        T        T           T            T   T             T   T             T   T             T T                           T   T   T   T                       T   T   T T   T                                          T   T   T   T   T   T   T  A    x OR y      B    x  AND y    C    x   D  x AND   y     E    y   F  x XOR y   G    x AND y     H  x AND y   I    x XOR y     J  y     K    x  OR y     L  x     M  x OR   y      N  x OR y

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The XOR definition is well known to be the odd-parity function  For two inputs   A XOR B    A AND NOT B  OR  B AND NOT A    The complement of XOR is XNOR   A XNOR B    A AND B  OR  NOT A AND NOT B   Henceforth  the normal two-input XAND defined as   A XAND B   A AND NOT B  The complement is XNAND   A XNAND B   B OR NOT A  A nice result from this XAND definition is that any dual-input binary function can be expressed concisely using no more than one logical function or gate                 --- --- --- ---     If A is    1   0   1   0     and B is    1   1   0   0                --- --- --- ---      Then         yields        ----------- --- --- --- ---    FALSE       0   0   0   0     A NOR B     0   0   0   1     A XAND B    0   0   1   0     NOT B       0   0   1   1     B XAND A    0   1   0   0     NOT A       0   1   0   1     A XOR B     0   1   1   0     A NAND B    0   1   1   1     A AND B     1   0   0   0     A XNOR B    1   0   0   1     A           1   0   1   0     B XNAND A   1   0   1   1     B           1   1   0   0     A XNAND B   1   1   0   1     A OR B      1   1   1   0     TRUE        1   1   1   1    ----------- --- --- --- ---    Note that XAND and XNAND lack reflexivity   This XNAND definition is extensible if we add numbered kinds of exclusive-ANDs to correspond to their corresponding minterms  Then XAND must have ceil lg n   or more inputs  with the unused msbs all zeroes  The normal kind of XAND is written without a number unless used in the context of other kinds    The various kinds of XAND or XNAND gates are useful for decoding    XOR is also extensible to any number of bits  The result is one if the number of ones is odd  and zero if even  If you complement any input or output bit of an XOR  the function becomes XNOR  and vice versa     I have seen no definition for XNOT  I will propose a definition   Let it to relate to high-impedance  Z  no signal  or perhaps null valued Boolean type Object    0xnot 0   Z 0xnot 1   Z 1xnot 0   1 1xnot 1   0

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First comes the logic  then the name  possibly patterned on previous naming   Thus 0 0 0  0 1 1  1 0 1  1 1 1 - for some reason this is called OR   Then 0-0 0  0-1 1  1-0 1  1-1 0 - it looks like OR except     let s call it XOR   Also 0 0 0  0 1 0  1 0 0  1 1 1 - for some reason this is called AND   Then 0 0 0  0 1 0  1 0 0  1 1 0 - it looks like AND except     let s call it XAND

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To add to this  since I was just dealing with it  if you are looking for an  equivalence gate  or a  coincedence gate  as your XAND  what you really have is just  equals    If you think about it  given XOR from above   F XOR F   F F XOR T   T T XOR F   T T XOR T   F   And we expect XAND should be   F XAND F   T F XAND T   F T XAND F   F T XAND T   T   And isn t this exactly the same   F    F   T F    T   F T    F   F T    T   T

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In most cases you won t find an Xand  Xor  nor  nand  Logical operator in programming  but fear not in most cases you can simulate it with the other operators    Since you didn t state any particular language  I won t do any specific language either  For my examples we ll use the following variables   A   3 B   5 C   7  and for code I ll put it in the code tag to make it easier to see what I did  I ll also follow the logic through the process to show what the end result will be   NAND  Also known as Not And  can easily be simulated by using a Not operator   normally indicated as      You can do the following  if    A gt B   amp  amp   B lt C        if    F amp  amp T     if   F     If T    In our example above it will be true  since both sides were not true  Thus giving us the desired result   NOR  Also known as Not OR  just like NAND we can simulate it with the not operator   if    A gt B      B lt C         if    F  T     if   T     if F    Again this will give us the desired outcomes   XOR   Xor or Exlcusive OR only will be true when one is TRUE but the Other is FALSE  If    A  gt  C  amp  amp  B  gt  A    amp  amp   A  gt  C    B  gt  A        If    F  amp  amp  T    amp  amp   F    T      If    F    amp  amp   T      If  T   amp  amp  T     If  T    So that is an example of it working for just 1 or the other being true  I ll show if both are true it will be false    If     A  lt  C  amp  amp  B  gt  A     amp  amp   A  lt  C    B  gt  A         If     T  amp  amp  T     amp  amp   T   T       If     T     amp  amp   T       If   F    amp  amp  T      If  F    And both false  If    A  gt  C  amp  amp  B  lt  A    amp  amp   A  gt  C    B  lt  A        If    F  amp  amp  F    amp  amp   F    F      If    F    amp  amp   F      If  T   amp  amp  F     If  F     And the picture to help   XAND  And finally our Exclusive And  this will only return true if both are sides are false  or if both are true   Of course You could just call this a Not XOR  NXOR   Both True If    A  lt  C  amp  amp  B  gt  A        A  lt  C    B  gt  A         If   T amp  amp T       T  T     IF  T     T    If  T    F    IF  T    Both False If    A  gt  C  amp  amp  B  lt  A        A  gt  C    B  lt  A         If     F  amp  amp  F       F   F     If   F     F    If   F    T    If  T    And lastly 1 true and the other one false  If   A  gt  C  amp  amp  B  gt  A       A  gt  C    B  gt  A        If   F  amp  amp  T        F    T      If  F    T     If  F  F    If  F       Or if you want to go the NXOR route     If      A  gt  C  amp  amp  B  gt  A    amp  amp   A  gt  C    B  gt  A        If      F  amp  amp  T    amp  amp   F    T       If      F    amp  amp   T       If    T   amp  amp  T      If    T     If  F      Of course everyone else s solutions probably state this as well  I am putting my own answer in here because the top answer didn t seem to understand that not all languages support XOR or XAND  for example C  uses   for XOR  and XAND isn t even supported    So I provided some examples of how to simulate it with the basic operators in the event your language doesn t support  XOR or XAND as their own operators like Php if   a XOR  B     As for Xnot what is that  Exclusive not  so not not  I don t know how that would look in a logic gate  I think it doesn t exist  Since Not just inverts the output from a 1 to a 0 and 0 to a 1    Anyway hope that helps

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Guys  don  t scare the crap out of others  hey  just kidding   but it  s really all a question of equivalences and synonyms   firstly    XAND  doesn  t exist logically  neither does  XNAND   however  XAND  is normally thought-up by a studious but confused initiating logic student  wow    It com from the thought that  if there  s a XOR exclusive OR  it  s logical to exist a  XAND   exclusive  AND   The rational suggestion would be an  IAND   inclusive  AND   which isn  t used or recognised as well  So        XNOR  lt   gt   XOR  lt   gt  EQV   And all this just discribes a unique operator  called the equivalency operator  lt     EQV  so   A     B    A  lt   gt  B   A XAND B   A XNOR B   A  XOR B     NOT A  AND B AND A AND NOT B    --------------------------------------------------------------------------------------- T     T       T          T          T          T                     T     T     F       F          F          F          F                     F     F     T       F          F          F          F                     F     F     F       T          T          T          T                     T       And just a closing comment  The  X  prefix is only possible if and only if the base operator isn  t unary  So  XNOR  lt    NOT XOR  lt      X NOR   Peace

[operators] What are XAND and XOR

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