Difference between revisions of "Template:Logic functions"
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imported>Sardanaphalus m (typo) |
imported>Sardanaphalus (table syntax/formatting) |
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| − | {| class="wikitable" style="text-align:center; | + | {| class="wikitable" style="margin:1.0em auto;text-align:center;" |
|- | |- | ||
| − | !rowspan=2 |''INPUT'' | + | !rowspan="2" style="width:6.0em;"| ''INPUT'' |
| − | !width | + | !style="width:6.0em;"| A !!style="width:20px;"| 0 !!style="width:20px;"| 0 !!style="width:20px;"| 1 !!style="width:20px;"| 1 |
| − | !width | + | |rowspan="2"| <!--(empty col)--> |
| − | !width | + | !rowspan="2"| Meaning |
| − | !width | ||
| − | |rowspan=2 |<!-- | ||
| − | !rowspan=2 | Meaning | ||
|- | |- | ||
| − | ! B | + | ! B !! 0 !! 1 !! 0 !! 1 |
| − | |||
|- | |- | ||
| − | |colspan=8|<!-- | + | |colspan="8"| <!--(empty line)--> |
|- | |- | ||
| − | !rowspan=16 | ''OUTPUT'' | + | !rowspan="16"| ''OUTPUT'' |
| FALSE || 0 || 0 || 0 || 0 | | FALSE || 0 || 0 || 0 || 0 | ||
| − | |rowspan=16 | | + | |rowspan="16"| |
| − | |align | + | |style="text-align:left;"| Whatever ''A'' and ''B'', output is false. [[Contradiction]]. |
|- | |- | ||
| A AND B || 0 || 0 || 0 || 1 | | A AND B || 0 || 0 || 0 || 1 | ||
| − | |align | + | |style="text-align:left;"| Output is true [[If and only if|if and only if (iff)]] both ''A'' and ''B'' are true. |
|- | |- | ||
| A <math>\not\rightarrow</math> B || 0 || 0 || 1 || 0 | | A <math>\not\rightarrow</math> B || 0 || 0 || 1 || 0 | ||
| − | |align | + | |style="text-align:left;"| ''A'' [[Material nonimplication|doesn't imply]] ''B''. True if ''A'' but not ''B''. |
|- | |- | ||
| A || 0 || 0 || 1 || 1 | | A || 0 || 0 || 1 || 1 | ||
| − | |align | + | |style="text-align:left;"| True whenever ''A'' is true. |
|- | |- | ||
| A <math>\not\leftarrow</math> B|| 0 || 1 || 0 || 0 | | A <math>\not\leftarrow</math> B|| 0 || 1 || 0 || 0 | ||
| − | |align | + | |style="text-align:left;"| ''A'' [[Converse nonimplication|is not implied by]] ''B''. True if not ''A'' but ''B''. |
|- | |- | ||
| B || 0 || 1 || 0 || 1 | | B || 0 || 1 || 0 || 1 | ||
| − | |align | + | |style="text-align:left;"| True whenever ''B'' is true. |
|- | |- | ||
| A XOR B || 0 || 1 || 1 || 0 | | A XOR B || 0 || 1 || 1 || 0 | ||
| − | |align | + | |style="text-align:left;"| True if ''A'' is not equal to ''B''. |
|- | |- | ||
| A OR B || 0 || 1 || 1 || 1 | | A OR B || 0 || 1 || 1 || 1 | ||
| − | |align | + | |style="text-align:left;"| True if ''A'' is true, or ''B'' is true, or both. |
|- | |- | ||
| A NOR B || 1 || 0 || 0 || 0 | | A NOR B || 1 || 0 || 0 || 0 | ||
| − | |align | + | |style="text-align:left;"| True if neither ''A'' nor ''B''. |
|- | |- | ||
| A XNOR B || 1 || 0 || 0 || 1 | | A XNOR B || 1 || 0 || 0 || 1 | ||
| − | |align | + | |style="text-align:left;"| True if ''A'' is equal to ''B''. |
|- | |- | ||
| NOT B || 1 || 0 || 1 || 0 | | NOT B || 1 || 0 || 1 || 0 | ||
| − | |align | + | |style="text-align:left;"| True if ''B'' is false. |
|- | |- | ||
| A <math>\leftarrow</math> B|| 1 || 0 || 1 || 1 | | A <math>\leftarrow</math> B|| 1 || 0 || 1 || 1 | ||
| − | |align | + | |style="text-align:left;"| ''A'' [[Converse implication|is implied by]] ''B''. False if not ''A'' but ''B'', otherwise true. |
|- | |- | ||
| NOT A || 1 || 1 || 0 || 0 | | NOT A || 1 || 1 || 0 || 0 | ||
| − | |align | + | |style="text-align:left;"| True if ''A'' is false. |
|- | |- | ||
| A <math>\rightarrow</math> B || 1 || 1 || 0 || 1 | | A <math>\rightarrow</math> B || 1 || 1 || 0 || 1 | ||
| − | |align | + | |style="text-align:left;"| ''A'' [[Material conditional|implies]] ''B''. False if ''A'' but not ''B'', otherwise true. |
|- | |- | ||
| A NAND B || 1 || 1 || 1 || 0 | | A NAND B || 1 || 1 || 1 || 0 | ||
| − | |align | + | |style="text-align:left;"| ''A'' and ''B'' are not both true. |
|- | |- | ||
| TRUE || 1 || 1 || 1 || 1 | | TRUE || 1 || 1 || 1 || 1 | ||
| − | |align | + | |style="text-align:left;"| Whatever ''A'' and ''B'', output is true. [[Tautology (logic)|Tautology]]. |
|- | |- | ||
|}<noinclude> | |}<noinclude> | ||
Revision as of 11:57, 28 November 2014
| INPUT | A | 0 | 0 | 1 | 1 | Meaning | |
|---|---|---|---|---|---|---|---|
| B | 0 | 1 | 0 | 1 | |||
| OUTPUT | FALSE | 0 | 0 | 0 | 0 | Whatever A and B, output is false. Contradiction. | |
| A AND B | 0 | 0 | 0 | 1 | Output is true if and only if (iff) both A and B are true. | ||
| A <math>\not\rightarrow</math> B | 0 | 0 | 1 | 0 | A doesn't imply B. True if A but not B. | ||
| A | 0 | 0 | 1 | 1 | True whenever A is true. | ||
| A <math>\not\leftarrow</math> B | 0 | 1 | 0 | 0 | A is not implied by B. True if not A but B. | ||
| B | 0 | 1 | 0 | 1 | True whenever B is true. | ||
| A XOR B | 0 | 1 | 1 | 0 | True if A is not equal to B. | ||
| A OR B | 0 | 1 | 1 | 1 | True if A is true, or B is true, or both. | ||
| A NOR B | 1 | 0 | 0 | 0 | True if neither A nor B. | ||
| A XNOR B | 1 | 0 | 0 | 1 | True if A is equal to B. | ||
| NOT B | 1 | 0 | 1 | 0 | True if B is false. | ||
| A <math>\leftarrow</math> B | 1 | 0 | 1 | 1 | A is implied by B. False if not A but B, otherwise true. | ||
| NOT A | 1 | 1 | 0 | 0 | True if A is false. | ||
| A <math>\rightarrow</math> B | 1 | 1 | 0 | 1 | A implies B. False if A but not B, otherwise true. | ||
| A NAND B | 1 | 1 | 1 | 0 | A and B are not both true. | ||
| TRUE | 1 | 1 | 1 | 1 | Whatever A and B, output is true. Tautology. | ||