1.AND Gate
three representations of an AND gate:
| A | B | AB |
|---|---|---|
| 0 | 1 | 0 |
| 1 | 1 | 1 |
| 1 | 0 | 0 |
AND means when and only when the two input values are both 1, the output is 1; otherwise, the output is 0 .
2.XOR Gate
three representations of an XOR gate
| A | B | A exclusive OR B |
|---|---|---|
| 1 | 0 | 1 |
| 0 | 0 | 0 |
| 1 | 1 | 1 |
XOR means when the two input values are different, the output is 1;otherwise, the output is 0.
3.
4.
| A | B | AB | A’ | AB XOR A’ |
|---|---|---|---|---|
| 0 | 0 | 0 | 1 | 1 |
| 0 | 1 | 0 | 1 | 1 |
| 1 | 0 | 0 | 0 | 0 |
| 1 | 1 | 1 | 0 | 1 |
5.
| A | B | AB | A’ | B’ | (AB)’ | A’+B’ |
|---|---|---|---|---|---|---|
| 0 | 0 | 0 | 1 | 1 | 1 | 1 |
| 0 | 1 | 0 | 1 | 0 | 1 | 1 |
| 1 | 0 | 0 | 0 | 1 | 1 | 1 |
| 1 | 1 | 1 | 0 | 0 | 0 | 0 |
因此(AB)′=A′+B′
6.
7.
i.(X8X7X6X5X4X3X2X1)2 or (00001111)2= (X8X7X6X51111)2
ii.(X8X7X6X5X4X3X2X1)2 xor (00001111) =(X8X7X6X5X4’X3’X2’X1’)2
iii.((X8X7X6X5X4X3X2X1)2 and (11110000)2) or (not(X8X7X6X5X4X3X2X1)2 and(00001111)2)=(X8X7X6X5X4’X3’X2’X1’)2