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Minimal negation operator (view source)

Revision as of 03:14, 23 August 2009

422 bytes removed ,  03:14, 23 August 2009
→‎Truth tables: redo table
Line 39: Line 39:  
<br>
 
<br>
   −
{| align="center" border="1" cellpadding="4" cellspacing="0" style="background:#f0f0ff; font-weight:bold; text-align:center; width:80%"
+
{| align="center" border="1" cellpadding="8" cellspacing="0" style="text-align:center; width:90%"
 
|+ <math>\text{Table 1.}~~\text{Logical Boundaries and Their Complements}</math>
 
|+ <math>\text{Table 1.}~~\text{Logical Boundaries and Their Complements}</math>
−
| width="20%" | <math>\mathcal{L}_1</math>
+
|- style="background:#f0f0ff"
−
| width="20%" | <math>\mathcal{L}_2</math>
+
| width="25%" | <math>\mathcal{L}_1</math>
−
| width="20%" | <math>\mathcal{L}_3</math>
+
| width="25%" | <math>\mathcal{L}_2</math>
−
| width="20%" | <math>\mathcal{L}_4</math>
+
| width="25%" | <math>\mathcal{L}_3</math>
−
|-
+
| width="25%" | <math>\mathcal{L}_4</math>
−
| Decimal
+
|- style="background:#f0f0ff"
−
| Binary
  −
| Sequential
  −
| Parenthetical
  −
|-
   
| &nbsp;
 
| &nbsp;
−
| align="right" | <math>p =\!</math>
+
| align="right" | <math>p\colon\!</math>
−
| 1 1 1 1 0 0 0 0
+
| <math>1~1~1~1~0~0~0~0</math>
 
| &nbsp;
 
| &nbsp;
−
|-
+
|- style="background:#f0f0ff"
 
| &nbsp;
 
| &nbsp;
−
| align="right" | <math>q =\!</math>
+
| align="right" | <math>q\colon\!</math>
−
| 1 1 0 0 1 1 0 0
+
| <math>1~1~0~0~1~1~0~0</math>
 
| &nbsp;
 
| &nbsp;
−
|-
+
|- style="background:#f0f0ff"
 
| &nbsp;
 
| &nbsp;
−
| align="right" | <math>r =\!</math>
+
| align="right" | <math>r\colon\!</math>
−
| 1 0 1 0 1 0 1 0
+
| <math>1~0~1~0~1~0~1~0</math>
 
| &nbsp;
 
| &nbsp;
−
|}
  −
{| align="center" border="1" cellpadding="4" cellspacing="0" style="background:ghostwhite; font-weight:bold; text-align:center; width:80%"
  −
|-
  −
| width="20%" | <math>f_{104}\!</math>
  −
| width="20%" | <math>f_{01101000}\!</math>
  −
| width="20%" | 0 1 1 0 1 0 0 0
  −
| width="20%" | <math>( p , q , r )\!</math>
  −
|-
  −
| <math>f_{148}\!</math>
  −
| <math>f_{10010100}\!</math>
  −
| 1 0 0 1 0 1 0 0
  −
| <math>( p , q , (r))\!</math>
  −
|-
  −
| <math>f_{146}\!</math>
  −
| <math>f_{10010010}\!</math>
  −
| 1 0 0 1 0 0 1 0
  −
| <math>( p , (q), r )\!</math>
  −
|-
  −
| <math>f_{97}\!</math>
  −
| <math>f_{01100001}\!</math>
  −
| 0 1 1 0 0 0 0 1
  −
| <math>( p , (q), (r))\!</math>
  −
|-
  −
| <math>f_{134}\!</math>
  −
| <math>f_{10000110}\!</math>
  −
| 1 0 0 0 0 1 1 0
  −
| <math>((p), q , r )\!</math>
  −
|-
  −
| <math>f_{73}\!</math>
  −
| <math>f_{01001001}\!</math>
  −
| 0 1 0 0 1 0 0 1
  −
| <math>((p), q , (r))\!</math>
  −
|-
  −
| <math>f_{41}\!</math>
  −
| <math>f_{00101001}\!</math>
  −
| 0 0 1 0 1 0 0 1
  −
| <math>((p), (q), r )\!</math>
  −
|-
  −
| <math>f_{22}\!</math>
  −
| <math>f_{00010110}\!</math>
  −
| 0 0 0 1 0 1 1 0
  −
| <math>((p), (q), (r))\!</math>
  −
|}
  −
{|  align="center" border="1" cellpadding="4" cellspacing="0" style="background:ghostwhite; font-weight:bold; text-align:center; width:80%"
  −
|-
  −
| width="20%" | <math>f_{233}\!</math>
  −
| width="20%" | <math>f_{11101001}\!</math>
  −
| width="20%" | 1 1 1 0 1 0 0 1
  −
| width="20%" | <math>(((p), (q), (r)))\!</math>
  −
|-
  −
| <math>f_{214}\!</math>
  −
| <math>f_{11010110}\!</math>
  −
| 1 1 0 1 0 1 1 0
  −
| <math>(((p), (q), r ))\!</math>
  −
|-
  −
| <math>f_{182}\!</math>
  −
| <math>f_{10110110}\!</math>
  −
| 1 0 1 1 0 1 1 0
  −
| <math>(((p), q , (r)))\!</math>
  −
|-
  −
| <math>f_{121}\!</math>
  −
| <math>f_{01111001}\!</math>
  −
| 0 1 1 1 1 0 0 1
  −
| <math>(((p), q , r ))\!</math>
  −
|-
  −
| <math>f_{158}\!</math>
  −
| <math>f_{10011110}\!</math>
  −
| 1 0 0 1 1 1 1 0
  −
| <math>(( p , (q), (r)))\!</math>
  −
|-
  −
| <math>f_{109}\!</math>
  −
| <math>f_{01101101}\!</math>
  −
| 0 1 1 0 1 1 0 1
  −
| <math>(( p , (q), r ))\!</math>
   
|-
 
|-
−
| <math>f_{107}\!</math>
+
|
−
| <math>f_{01101011}\!</math>
+
<math>\begin{matrix}
−
| 0 1 1 0 1 0 1 1
+
f_{104}
−
| <math>(( p , q , (r)))\!</math>
+
\\[4pt]
 +
f_{148}
 +
\\[4pt]
 +
f_{146}
 +
\\[4pt]
 +
f_{97}
 +
\\[4pt]
 +
f_{134}
 +
\\[4pt]
 +
f_{73}
 +
\\[4pt]
 +
f_{41}
 +
\\[4pt]
 +
f_{22}
 +
\end{matrix}</math>
 +
|
 +
<math>\begin{matrix}
 +
f_{01101000}
 +
\\[4pt]
 +
f_{10010100}
 +
\\[4pt]
 +
f_{10010010}
 +
\\[4pt]
 +
f_{01100001}
 +
\\[4pt]
 +
f_{10000110}
 +
\\[4pt]
 +
f_{01001001}
 +
\\[4pt]
 +
f_{00101001}
 +
\\[4pt]
 +
f_{00010110}
 +
\end{matrix}</math>
 +
|
 +
<math>\begin{matrix}
 +
0~1~1~0~1~0~0~0
 +
\\[4pt]
 +
1~0~0~1~0~1~0~0
 +
\\[4pt]
 +
1~0~0~1~0~0~1~0
 +
\\[4pt]
 +
0~1~1~0~0~0~0~1
 +
\\[4pt]
 +
1~0~0~0~0~1~1~0
 +
\\[4pt]
 +
0~1~0~0~1~0~0~1
 +
\\[4pt]
 +
0~0~1~0~1~0~0~1
 +
\\[4pt]
 +
0~0~0~1~0~1~1~0
 +
\end{matrix}</math>
 +
|
 +
<math>\begin{matrix}
 +
( p , q , r )
 +
\\[4pt]
 +
( p , q , (r))
 +
\\[4pt]
 +
( p , (q), r )
 +
\\[4pt]
 +
( p , (q), (r))
 +
\\[4pt]
 +
((p), q , r )
 +
\\[4pt]
 +
((p), q , (r))
 +
\\[4pt]
 +
((p), (q), r )
 +
\\[4pt]
 +
((p), (q), (r))
 +
\end{matrix}</math>
 
|-
 
|-
−
| <math>f_{151}\!</math>
+
|
−
| <math>f_{10010111}\!</math>
+
<math>\begin{matrix}
−
| 1 0 0 1 0 1 1 1
+
f_{233}
−
| <math>(( p , q , r ))\!</math>
+
\\[4pt]
 +
f_{214}
 +
\\[4pt]
 +
f_{182}
 +
\\[4pt]
 +
f_{121}
 +
\\[4pt]
 +
f_{158}
 +
\\[4pt]
 +
f_{109}
 +
\\[4pt]
 +
f_{107}
 +
\\[4pt]
 +
f_{151}
 +
\end{matrix}</math>
 +
|
 +
<math>\begin{matrix}
 +
f_{11101001}
 +
\\[4pt]
 +
f_{11010110}
 +
\\[4pt]
 +
f_{10110110}
 +
\\[4pt]
 +
f_{01111001}
 +
\\[4pt]
 +
f_{10011110}
 +
\\[4pt]
 +
f_{01101101}
 +
\\[4pt]
 +
f_{01101011}
 +
\\[4pt]
 +
f_{10010111}
 +
\end{matrix}</math>
 +
|
 +
<math>\begin{matrix}
 +
1~1~1~0~1~0~0~1
 +
\\[4pt]
 +
1~1~0~1~0~1~1~0
 +
\\[4pt]
 +
1~0~1~1~0~1~1~0
 +
\\[4pt]
 +
0~1~1~1~1~0~0~1
 +
\\[4pt]
 +
1~0~0~1~1~1~1~0
 +
\\[4pt]
 +
0~1~1~0~1~1~0~1
 +
\\[4pt]
 +
0~1~1~0~1~0~1~1
 +
\\[4pt]
 +
1~0~0~1~0~1~1~1
 +
\end{matrix}</math>
 +
|
 +
<math>\begin{matrix}
 +
(((p), (q), (r)))
 +
\\[4pt]
 +
(((p), (q), r ))
 +
\\[4pt]
 +
(((p), q , (r)))
 +
\\[4pt]
 +
(((p), q , r ))
 +
\\[4pt]
 +
(( p , (q), (r)))
 +
\\[4pt]
 +
(( p , (q), r ))
 +
\\[4pt]
 +
(( p , q , (r)))
 +
\\[4pt]
 +
(( p , q , r ))
 +
\end{matrix}</math>
 
|}
 
|}
  
Jon Awbrey
12,080

edits

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