Combining gates
Circuit components which take several inputs, compare the inputs with each other, and provide a single output based on logical functions such as AND, OR and NOT. are often combined to create more complex conditions. When this happens, the Data which is sent out of a system. of one gate is connected directly to another gate.
Combining an OR gate with a NOT gate
The expression from the circuit can be written as:
Q = ( A + B )
Here, the output Q is 1 (TRUE) only if inputs A and B are 0 (FALSE)
| A | B | C = A + B | Q |
| 0 | 0 | 0 | 1 |
| 0 | 1 | 1 | 0 |
| 1 | 0 | 1 | 0 |
| 1 | 1 | 1 | 0 |
| A | 0 |
|---|---|
| B | 0 |
| C = A + B | 0 |
| Q | 1 |
| A | 0 |
|---|---|
| B | 1 |
| C = A + B | 1 |
| Q | 0 |
| A | 1 |
|---|---|
| B | 0 |
| C = A + B | 1 |
| Q | 0 |
| A | 1 |
|---|---|
| B | 1 |
| C = A + B | 1 |
| Q | 0 |
Note: C is not strictly necessary in the table, but it helps in understanding Q.
Combining two AND gates
The expression from the circuit can be written as:
Q = (( A · B ) · C )
Here, the output Q is 1 (TRUE) only if Data which is inserted into a system for processing and/or storage. C and D are 1 (TRUE). D is only 1 (TRUE) if inputs A and B are 1 (TRUE).
As a A table to list the output for all possible input combinations into a logic gate. this circuit is:
| A | B | C | D = A · B | Q |
| 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 |
| 0 | 1 | 1 | 0 | 0 |
| 1 | 0 | 0 | 0 | 0 |
| 1 | 0 | 1 | 0 | 0 |
| 1 | 1 | 0 | 1 | 0 |
| 1 | 1 | 1 | 1 | 1 |
| A | 0 |
|---|---|
| B | 0 |
| C | 0 |
| D = A · B | 0 |
| Q | 0 |
| A | 0 |
|---|---|
| B | 0 |
| C | 1 |
| D = A · B | 0 |
| Q | 0 |
| A | 0 |
|---|---|
| B | 1 |
| C | 0 |
| D = A · B | 0 |
| Q | 0 |
| A | 0 |
|---|---|
| B | 1 |
| C | 1 |
| D = A · B | 0 |
| Q | 0 |
| A | 1 |
|---|---|
| B | 0 |
| C | 0 |
| D = A · B | 0 |
| Q | 0 |
| A | 1 |
|---|---|
| B | 0 |
| C | 1 |
| D = A · B | 0 |
| Q | 0 |
| A | 1 |
|---|---|
| B | 1 |
| C | 0 |
| D = A · B | 1 |
| Q | 0 |
| A | 1 |
|---|---|
| B | 1 |
| C | 1 |
| D = A · B | 1 |
| Q | 1 |
Note: D is not strictly necessary in the table, but it helps in understanding Q.
Combining an AND gate with an OR gate
The expression from the circuit can be written as:
Q = (( A · B ) + C )
Here, the output Q is 1 (TRUE) only if Data which is inserted into a system for processing and/or storage. C or D are 1 (TRUE). D is only 1 (TRUE) if inputs A and B are 1 (TRUE).
As a A table to list the output for all possible input combinations into a logic gate. this circuit is:
| A | B | C | D = A · B | Q |
| 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 1 |
| 0 | 1 | 0 | 0 | 0 |
| 0 | 1 | 1 | 0 | 1 |
| 1 | 0 | 0 | 0 | 0 |
| 1 | 0 | 1 | 0 | 1 |
| 1 | 1 | 0 | 1 | 1 |
| 1 | 1 | 1 | 1 | 1 |
| A | 0 |
|---|---|
| B | 0 |
| C | 0 |
| D = A · B | 0 |
| Q | 0 |
| A | 0 |
|---|---|
| B | 0 |
| C | 1 |
| D = A · B | 0 |
| Q | 1 |
| A | 0 |
|---|---|
| B | 1 |
| C | 0 |
| D = A · B | 0 |
| Q | 0 |
| A | 0 |
|---|---|
| B | 1 |
| C | 1 |
| D = A · B | 0 |
| Q | 1 |
| A | 1 |
|---|---|
| B | 0 |
| C | 0 |
| D = A · B | 0 |
| Q | 0 |
| A | 1 |
|---|---|
| B | 0 |
| C | 1 |
| D = A · B | 0 |
| Q | 1 |
| A | 1 |
|---|---|
| B | 1 |
| C | 0 |
| D = A · B | 1 |
| Q | 1 |
| A | 1 |
|---|---|
| B | 1 |
| C | 1 |
| D = A · B | 1 |
| Q | 1 |
Note: D is not strictly necessary in the table, but it helps in understanding Q.
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