6.4 - Logic Gates
- a boolean variable X has 2 outcomes (True/False) or (1/0)
Truth Tables
OR
\[Q = X + Y\]
| X |
Y |
Q |
| 0 |
0 |
0 |
| 0 |
1 |
1 |
| 1 |
0 |
1 |
| 1 |
1 |
1 |
AND
\[Q=XY\]
| X |
Y |
Q |
| 0 |
0 |
0 |
| 0 |
1 |
0 |
| 1 |
0 |
0 |
| 1 |
1 |
1 |
NOT
\[Q = \overline{X}\]
NAND
\[Q=\overline{XY}\]
| X |
Y |
Q |
| 0 |
0 |
1 |
| 0 |
1 |
1 |
| 1 |
0 |
1 |
| 1 |
1 |
0 |
NOR
\[Q=\overline{X+Y}\]
| X |
Y |
Q |
| 0 |
0 |
1 |
| 0 |
1 |
0 |
| 1 |
0 |
0 |
| 1 |
1 |
0 |
XOR
\[Q=X\overline{Y}+\overline{X}Y\]
\[Q=X\otimes{Y}\]
| X |
Y |
Q |
| 0 |
0 |
0 |
| 0 |
1 |
1 |
| 1 |
0 |
1 |
| 1 |
1 |
0 |
Half-Adder
| A |
B |
A+B |
C (carry) |
| 0 |
0 |
0 |
0 |
| 0 |
1 |
1 |
0 |
| 1 |
0 |
1 |
0 |
| 1 |
1 |
0 |
1 |
NB:
\[A + B = A \otimes{B}\]
\[C=AB\]