Let's look at a more complex truth table. To do this, we will add more columns instead of immediately jumping to the answer.
Table 1 shows the truth table for Q = (A XOR B) AND NOT(C).
Table 1
| A (in) | B (in) | C (in) | A XOR B | NOT(C) | Q (out) |
|---|---|---|---|---|---|
0 |
0 |
0 |
0 |
1 |
0 |
0 |
0 |
1 |
0 |
0 |
0 |
0 |
1 |
0 |
1 |
1 |
1 |
0 |
1 |
1 |
1 |
0 |
0 |
1 |
0 |
0 |
1 |
1 |
1 |
1 |
0 |
1 |
1 |
0 |
0 |
1 |
1 |
0 |
0 |
1 |
0 |
1 |
1 |
1 |
0 |
0 |
0 |
Note that the input columns still count up in binary (000, 001, 010, ...) even though we have
three of them instead of two.
How many rows will a truth table with n inputs have?
2n (because we're effectively counting in binary with the inputs)