How logic truth tables work out.
| 0 | 0 | 1 | 1 | a |
| 0 | 1 | 0 | 1 | b |
| 0 | 0 | 0 | 0 | FALSE (0) |
| 0 | 0 | 0 | 1 | a AND b |
| 0 | 0 | 1 | 0 | NOT(a IMPLIES b) |
| 0 | 0 | 1 | 1 | a |
| 0 | 1 | 0 | 0 | NOT(b IMPLIES a) |
| 0 | 1 | 0 | 1 | b |
| 0 | 1 | 1 | 0 | a XOR b |
| 0 | 1 | 1 | 1 | a OR b |
| 1 | 0 | 0 | 0 | a NOR b |
| 1 | 0 | 0 | 1 | a EQUAL b |
| 1 | 0 | 1 | 0 | NOT b |
| 1 | 0 | 1 | 1 | b IMPLIES a |
| 1 | 1 | 0 | 0 | NOT a |
| 1 | 1 | 0 | 1 | a IMPLIES b |
| 1 | 1 | 1 | 0 | a NAND b |
| 1 | 1 | 1 | 1 | TRUE (1) |