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.
C = A
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.
C = A
Answers
GPT-4o mini
Let's break down the logic you've described:
1. **Input Variables**:
- A (can be 0 or 1)
- B (can be 0 or 1)
2. **Output C**:
- The output C is true (1) if A and B are different (this condition alone gives C = 1 for A=0, B=1 or A=1, B=0).
- Additionally, if A is true (1), then output C must also be 1.
- In all other cases, the output is false (0).
### Formulating the Conditions
1. If A and B are different, we can represent this condition with:
- \( A \neq B \) which can also be expressed as \( (A \land \neg B) \lor (\neg A \land B) \)
2. If A is true (1), the output C must also be true. This reinforces the output to be true when A is 1, regardless of B.
3. The output C can be summarized logically as:
- C = (A ≠ B) OR (A AND 1)
- However, since \( A \) itself represents true or false when 1 or 0, the output can simply be expressed by the condition:
- C = (A AND 1) OR (A XOR B)
### Truth Table
Now, let's construct the truth table for inputs A and B based on the above logic.
| A | B | A ≠ B | C |
|---|---|-------|---|
| 0 | 0 | 0 | 0 |
| 0 | 1 | 1 | 1 |
| 1 | 0 | 1 | 1 |
| 1 | 1 | 0 | 1 |
### Explanation of the Truth Table:
- **Row 1**: A = 0, B = 0 → A and B are not different (A ≠ B = 0) and also A is false. Thus, C = 0.
- **Row 2**: A = 0, B = 1 → A and B are different (A ≠ B = 1). C = 1.
- **Row 3**: A = 1, B = 0 → A and B are different (A ≠ B = 1). C = 1.
- **Row 4**: A = 1, B = 1 → A and B are not different (A ≠ B = 0) but A is true. Thus, C = 1.
### Logic Expression
From the truth table, we can derive the logic expression for the output C:
1. C = (A AND 1) OR (A XOR B)
But since \( A AND 1 \) is simply A, we can write this expression as:
- C = A + (A XOR B)
Thus, the final expression that fits your logic circuit based on the rules and the truth table is:
- C = A + (A XOR B)
Please let me know if you need any further assistance!
1. **Input Variables**:
- A (can be 0 or 1)
- B (can be 0 or 1)
2. **Output C**:
- The output C is true (1) if A and B are different (this condition alone gives C = 1 for A=0, B=1 or A=1, B=0).
- Additionally, if A is true (1), then output C must also be 1.
- In all other cases, the output is false (0).
### Formulating the Conditions
1. If A and B are different, we can represent this condition with:
- \( A \neq B \) which can also be expressed as \( (A \land \neg B) \lor (\neg A \land B) \)
2. If A is true (1), the output C must also be true. This reinforces the output to be true when A is 1, regardless of B.
3. The output C can be summarized logically as:
- C = (A ≠ B) OR (A AND 1)
- However, since \( A \) itself represents true or false when 1 or 0, the output can simply be expressed by the condition:
- C = (A AND 1) OR (A XOR B)
### Truth Table
Now, let's construct the truth table for inputs A and B based on the above logic.
| A | B | A ≠ B | C |
|---|---|-------|---|
| 0 | 0 | 0 | 0 |
| 0 | 1 | 1 | 1 |
| 1 | 0 | 1 | 1 |
| 1 | 1 | 0 | 1 |
### Explanation of the Truth Table:
- **Row 1**: A = 0, B = 0 → A and B are not different (A ≠ B = 0) and also A is false. Thus, C = 0.
- **Row 2**: A = 0, B = 1 → A and B are different (A ≠ B = 1). C = 1.
- **Row 3**: A = 1, B = 0 → A and B are different (A ≠ B = 1). C = 1.
- **Row 4**: A = 1, B = 1 → A and B are not different (A ≠ B = 0) but A is true. Thus, C = 1.
### Logic Expression
From the truth table, we can derive the logic expression for the output C:
1. C = (A AND 1) OR (A XOR B)
But since \( A AND 1 \) is simply A, we can write this expression as:
- C = A + (A XOR B)
Thus, the final expression that fits your logic circuit based on the rules and the truth table is:
- C = A + (A XOR B)
Please let me know if you need any further assistance!