Question
Design some logic with the following rules:
Two inputs are A and B
The output is C
The logic is as follows: If A and B are diferent values, the output is true
(1). In addiion, if A is true (1) then the output is true (1). Otherwise, the
output is false (0).
Build the Truth Table for this logic circuit. Using the Truth Table write the logic expression for this funcion.
Another way to say this instead of using xor
Two inputs are A and B
The output is C
The logic is as follows: If A and B are diferent values, the output is true
(1). In addiion, if A is true (1) then the output is true (1). Otherwise, the
output is false (0).
Build the Truth Table for this logic circuit. Using the Truth Table write the logic expression for this funcion.
Another way to say this instead of using xor
Answers
GPT-4o mini
To solve the problem, we will first summarize the rules provided and then build a truth table. Finally, we'll derive the logic expression based on the truth table.
### Given Rules:
1. If \( A \) and \( B \) are different values, the output is true (1).
2. If \( A \) is true (1), then the output is also true (1).
3. Otherwise, the output is false (0).
### Interpretation of Rules:
- Rule 1 indicates that if \( A \) and \( B \) are different, the output will be true, which is similar to the XOR operation.
- Rule 2 indicates that when \( A \) is true, the output should be true regardless of \( B \).
- Rule 3 indicates that if both conditions are not met, the output will be false.
### Constructing the Truth Table
Let's create a truth table for the inputs \( A \) and \( B \).
| A | B | A XOR B | Output (C) |
|---|---|---------|------------|
| 0 | 0 | 0 | 0 |
| 0 | 1 | 1 | 1 |
| 1 | 0 | 1 | 1 |
| 1 | 1 | 0 | 1 |
### Explanation of the Output (C)
1. **When both A and B are 0**: They are the same, so output is 0.
2. **When A is 0 and B is 1**: They are different, so output is 1.
3. **When A is 1 and B is 0**: They are different, so output is 1.
4. **When both A and B are 1**: Since A is true, output is also true (1).
### Final Truth Table with Detailed Outputs
| A | B | C |
|---|---|----|
| 0 | 0 | 0 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 1 |
### Logic Expression for Output (C)
From the truth table, we can derive the logic expression:
C can be expressed with the following conditions:
1. \( C = (A \oplus B) + A \)
Where \( A \oplus B \) represents the XOR operation, and '+' represents the logical OR operation.
### Alternative Description:
Instead of using the term "XOR", this logic can be defined as "A is true if either A is true or A and B are different."
### Summary
- The output \( C \) is true (1) if:
- \( A \) and \( B \) are different, or
- \( A \) is true.
- The final logic expression is: \( C = (A \oplus B) + A \).
### Given Rules:
1. If \( A \) and \( B \) are different values, the output is true (1).
2. If \( A \) is true (1), then the output is also true (1).
3. Otherwise, the output is false (0).
### Interpretation of Rules:
- Rule 1 indicates that if \( A \) and \( B \) are different, the output will be true, which is similar to the XOR operation.
- Rule 2 indicates that when \( A \) is true, the output should be true regardless of \( B \).
- Rule 3 indicates that if both conditions are not met, the output will be false.
### Constructing the Truth Table
Let's create a truth table for the inputs \( A \) and \( B \).
| A | B | A XOR B | Output (C) |
|---|---|---------|------------|
| 0 | 0 | 0 | 0 |
| 0 | 1 | 1 | 1 |
| 1 | 0 | 1 | 1 |
| 1 | 1 | 0 | 1 |
### Explanation of the Output (C)
1. **When both A and B are 0**: They are the same, so output is 0.
2. **When A is 0 and B is 1**: They are different, so output is 1.
3. **When A is 1 and B is 0**: They are different, so output is 1.
4. **When both A and B are 1**: Since A is true, output is also true (1).
### Final Truth Table with Detailed Outputs
| A | B | C |
|---|---|----|
| 0 | 0 | 0 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 1 |
### Logic Expression for Output (C)
From the truth table, we can derive the logic expression:
C can be expressed with the following conditions:
1. \( C = (A \oplus B) + A \)
Where \( A \oplus B \) represents the XOR operation, and '+' represents the logical OR operation.
### Alternative Description:
Instead of using the term "XOR", this logic can be defined as "A is true if either A is true or A and B are different."
### Summary
- The output \( C \) is true (1) if:
- \( A \) and \( B \) are different, or
- \( A \) is true.
- The final logic expression is: \( C = (A \oplus B) + A \).