Send
Close Add comments:
(status displays here)
Got it! This site uses cookies. You consent to this by clicking on "Got it!" or by continuing to use this website.nbsp; Note: This appears on each machine/browser from which this site is accessed.
NOR operator
1. NOR operator
2. Tree representation
3. Nand operator
The Nor, for negative-or, operator is expressed as follows.
X !| Y
4. Extended truth table
Here is the extended truth table.
X Y | X !| Y
------------
0 0 | 0 1 0
0 1 | 0 0 1
1 0 | 1 0 0
1 1 | 1 0 1
5. JSON prefix tree
Here is a one way to represent a pretty-printed prefix tree in JSON list form.
["op2","nor",
["var","X"],
["var","Y"]
]
6. Equivalence
The logical or "
|" is equivalent to the following, using Nand operators.
X Y | ( ( X !& X ) !& ( Y !& Y ) ) !& ( ( X !& X ) !& ( Y !& Y ) )
------------------------------------------------------------------
0 0 | ( ( 0 1 0 ) 0 ( 0 1 0 ) ) 1 ( ( 0 1 0 ) 0 ( 0 1 0 ) )
0 1 | ( ( 0 1 0 ) 1 ( 1 0 1 ) ) 0 ( ( 0 1 0 ) 1 ( 1 0 1 ) )
1 0 | ( ( 1 0 1 ) 1 ( 0 1 0 ) ) 0 ( ( 1 0 1 ) 1 ( 0 1 0 ) )
1 1 | ( ( 1 0 1 ) 1 ( 1 0 1 ) ) 0 ( ( 1 0 1 ) 1 ( 1 0 1 ) )
7. JSON prefix tree
Here is a one way to represent a pretty-printed prefix tree in JSON list form.
["op2","nand",
["op2","nand",
["op2","nand",
["var","X"],
["var","X"]
],
["op2","nand",
["var","Y"],
["var","Y"]
]
],
["op2","nand",
["op2","nand",
["var","X"],
["var","X"]
],
["op2","nand",
["var","Y"],
["var","Y"]
]
]
]
8. Proof
Here is the proof.
X Y | ( X !| Y ) = ( ( ( X !& X ) !& ( Y !& Y ) ) !& ( ( X !& X ) !& ( Y !& Y ) ) )
-----------------------------------------------------------------------------------
0 0 | ( 0 1 0 ) 1 ( ( ( 0 1 0 ) 0 ( 0 1 0 ) ) 1 ( ( 0 1 0 ) 0 ( 0 1 0 ) ) )
0 1 | ( 0 0 1 ) 1 ( ( ( 0 1 0 ) 1 ( 1 0 1 ) ) 0 ( ( 0 1 0 ) 1 ( 1 0 1 ) ) )
1 0 | ( 1 0 0 ) 1 ( ( ( 1 0 1 ) 1 ( 0 1 0 ) ) 0 ( ( 1 0 1 ) 1 ( 0 1 0 ) ) )
1 1 | ( 1 0 1 ) 1 ( ( ( 1 0 1 ) 1 ( 1 0 1 ) ) 0 ( ( 1 0 1 ) 1 ( 1 0 1 ) ) )
9. JSON prefix tree
Here is a one way to represent a pretty-printed prefix tree in JSON list form.
["op2","eq",
["op2","nor",
["var","X"],
["var","Y"]
],
["op2","nand",
["op2","nand",
["op2","nand",
["var","X"],
["var","X"]
],
["op2","nand",
["var","Y"],
["var","Y"]
]
],
["op2","nand",
["op2","nand",
["var","X"],
["var","X"]
],
["op2","nand",
["var","Y"],
["var","Y"]
]
]
]
]
10. End of page
