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.
Does C = A work
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.
Does C = A work
Answers
GPT-4o mini
To design this logic based on the specified rules, we need to analyze the conditions and construct the truth table step by step.
### Rules Summary:
1. If A and B are different values (i.e., one is 0 and the other is 1), then C should output true (1).
2. If A is true (1), then C should also be true (1). If A is false (0), the output should be false (0).
### Truth Table Construction
Let’s denote A and B as inputs, and C as the output. The values for A and B will be either 0 or 1. We'll compute C based on the given rules.
| A | B | A ≠ B (Rule 1) | A (Rule 2) | C (Output) |
|---|---|-----------------|-----------|------------|
| 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 1 | 0 | 1 |
| 1 | 0 | 1 | 1 | 1 |
| 1 | 1 | 0 | 1 | 1 |
### Explanation of Outputs:
- When **A = 0** and **B = 0**: Both values are the same, so C = 0.
- When **A = 0** and **B = 1**: A and B are different; however, A is 0, so C = 1.
- When **A = 1** and **B = 0**: A is true, so C = 1 regardless of B.
- When **A = 1** and **B = 1**: A is true, so C = 1, regardless of B.
### Final Truth Table Summary:
| A | B | C |
|---|---|---|
| 0 | 0 | 0 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 1 |
### Logic Expression
From the truth table, we can derive the logic expression for C. Based on our observations:
- C is 1 in the following cases:
- B = 1 and A = 0 (Rule 1)
- A = 1 (it does not matter what B is)
Thus, the logic expression for C can be formulated as:
\[ C = A + (\overline{A} \cdot B) \]
Where:
- \( A \) represents the case when A is true.
- \( \overline{A} \) represents the negation of A (A is false).
- The term \( \overline{A} \cdot B \) represents the specific case when A is false and B is true.
### Conclusion
The statement "Does C = A work?" is **not correct**. The output C is not equal to A in all cases, as we saw in the truth table where C takes on different values depending on B. The correct expression to calculate C is using \( C = A + (\overline{A} \cdot B) \).
### Rules Summary:
1. If A and B are different values (i.e., one is 0 and the other is 1), then C should output true (1).
2. If A is true (1), then C should also be true (1). If A is false (0), the output should be false (0).
### Truth Table Construction
Let’s denote A and B as inputs, and C as the output. The values for A and B will be either 0 or 1. We'll compute C based on the given rules.
| A | B | A ≠ B (Rule 1) | A (Rule 2) | C (Output) |
|---|---|-----------------|-----------|------------|
| 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 1 | 0 | 1 |
| 1 | 0 | 1 | 1 | 1 |
| 1 | 1 | 0 | 1 | 1 |
### Explanation of Outputs:
- When **A = 0** and **B = 0**: Both values are the same, so C = 0.
- When **A = 0** and **B = 1**: A and B are different; however, A is 0, so C = 1.
- When **A = 1** and **B = 0**: A is true, so C = 1 regardless of B.
- When **A = 1** and **B = 1**: A is true, so C = 1, regardless of B.
### Final Truth Table Summary:
| A | B | C |
|---|---|---|
| 0 | 0 | 0 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 1 |
### Logic Expression
From the truth table, we can derive the logic expression for C. Based on our observations:
- C is 1 in the following cases:
- B = 1 and A = 0 (Rule 1)
- A = 1 (it does not matter what B is)
Thus, the logic expression for C can be formulated as:
\[ C = A + (\overline{A} \cdot B) \]
Where:
- \( A \) represents the case when A is true.
- \( \overline{A} \) represents the negation of A (A is false).
- The term \( \overline{A} \cdot B \) represents the specific case when A is false and B is true.
### Conclusion
The statement "Does C = A work?" is **not correct**. The output C is not equal to A in all cases, as we saw in the truth table where C takes on different values depending on B. The correct expression to calculate C is using \( C = A + (\overline{A} \cdot B) \).