What are XAND and XOR? Also is there an XNot
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
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.
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
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.
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.
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