Expiain this circuits in detail EQU 1 wy''

Introductory Circuit Analysis (13th Edition)
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Author:Robert L. Boylestad
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## Explain this circuit in detail

### EQU 1

The provided image shows a logic circuit diagram. Below is a detailed description of its components and how they are connected.

### Components:
1. **Inputs:**
    - Three input variables labeled as \( x \), \( y \), and \( z \).

2. **Gates:**
    - **AND Gate**: This gate outputs true only if all its inputs are true.
    - **OR Gate**: This gate outputs true if at least one of its inputs is true.
    - **NOT Gate (Inverter)**: This gate outputs the inverse of its input.
    
3. **Output:**
    - A light bulb used to represent the final output of the circuit.

### Connections and Function:

1. **Input Variables:**
    - The variables \( x \), \( y \), and \( z \) are fed into the inputs of various gates.

2. **First Branch:**
   - \( x \) is connected to the input of an AND gate.
   - \( y \) is also connected to the second input of the same AND gate.
   - The output of this AND gate represents \( x \cdot y \), which is fed into an OR gate. 
   
3. **Second Branch:**
   - \( x \) is again fed into a NOT gate.
   - The output of this NOT gate (\( \neg x \)) is fed into an OR gate along with \( z \).

4. **Combining Outputs:**
   - The outputs of the two OR gates:
     - Output from the first branch: \( x \cdot y \)
     - Output from the second branch: \( \neg x \cdot z \)
    
5. **Final Output:**
   - The outputs from the OR gates are combined in an OR gate.
   - The final output from this OR gate will light up the bulb if:
     - \( x \cdot y = 1 \) or \( \neg x \cdot z = 1 \)
   - This can be summarized as the Boolean expression:
     \[
     (x \cdot y) + (\neg x \cdot z)
     \]

The function of this circuit is to check if any of the combined conditions of the inputs are true to light up the bulb. If so, the light bulb will turn on, indicating a true output for the
Transcribed Image Text:## Explain this circuit in detail ### EQU 1 The provided image shows a logic circuit diagram. Below is a detailed description of its components and how they are connected. ### Components: 1. **Inputs:** - Three input variables labeled as \( x \), \( y \), and \( z \). 2. **Gates:** - **AND Gate**: This gate outputs true only if all its inputs are true. - **OR Gate**: This gate outputs true if at least one of its inputs is true. - **NOT Gate (Inverter)**: This gate outputs the inverse of its input. 3. **Output:** - A light bulb used to represent the final output of the circuit. ### Connections and Function: 1. **Input Variables:** - The variables \( x \), \( y \), and \( z \) are fed into the inputs of various gates. 2. **First Branch:** - \( x \) is connected to the input of an AND gate. - \( y \) is also connected to the second input of the same AND gate. - The output of this AND gate represents \( x \cdot y \), which is fed into an OR gate. 3. **Second Branch:** - \( x \) is again fed into a NOT gate. - The output of this NOT gate (\( \neg x \)) is fed into an OR gate along with \( z \). 4. **Combining Outputs:** - The outputs of the two OR gates: - Output from the first branch: \( x \cdot y \) - Output from the second branch: \( \neg x \cdot z \) 5. **Final Output:** - The outputs from the OR gates are combined in an OR gate. - The final output from this OR gate will light up the bulb if: - \( x \cdot y = 1 \) or \( \neg x \cdot z = 1 \) - This can be summarized as the Boolean expression: \[ (x \cdot y) + (\neg x \cdot z) \] The function of this circuit is to check if any of the combined conditions of the inputs are true to light up the bulb. If so, the light bulb will turn on, indicating a true output for the
## Understanding NOT and XOR Gates

### Explanation of the Circuit

This circuit diagram involves the use of NOT and XOR gates to process two inputs labeled \( A \) and \( B \). These inputs are typically binary, meaning they can either be 0 (off) or 1 (on).

### Components:

1. **Inputs:**
    - \( A \): The first binary input.
    - \( B \): The second binary input.
    
2. **NOT Gate:**
    - A NOT gate inverts the input signal; if the input is 1, the output will be 0 and vice versa.

3. **XOR Gate:**
    - An XOR (Exclusive OR) gate outputs true or 1 only when the number of true inputs is odd. For two inputs, it outputs 1 when exactly one of the inputs is 1.

### Circuit Diagram:

The diagram illustrates a circuit comprised of two main logic gates:
1. **NOT Gate Operation**: Not explicitly shown as an individual gate here, but let's assume it processes one of the inputs, say \( A \), before feeding into the XOR gate.
2. **XOR Gate Connections**:
    - The inputs \( A \) and \( B \) are connected to the XOR gate.
    - The output of the XOR gate then powers the bulb.

### Bulb Illumination (Output):

The bulb will light up based on the output from the XOR gate. The XOR gate's output logic is as follows:
- If \( A = 0 \) and \( B = 0 \), XOR Output is \( 0 \); the bulb does not light up.
- If \( A = 0 \) and \( B = 1 \), XOR Output is \( 1 \); the bulb lights up.
- If \( A = 1 \) and \( B = 0 \), XOR Output is \( 1 \); the bulb lights up.
- If \( A = 1 \) and \( B = 1 \), XOR Output is \( 0 \); the bulb does not light up.

### Conclusion

This simple circuit effectively demonstrates the role of XOR gates in digital logic. By understanding each gate's function, one can predict the circuit's output for various input states, highlighting fundamental principles in digital electronics.
Transcribed Image Text:## Understanding NOT and XOR Gates ### Explanation of the Circuit This circuit diagram involves the use of NOT and XOR gates to process two inputs labeled \( A \) and \( B \). These inputs are typically binary, meaning they can either be 0 (off) or 1 (on). ### Components: 1. **Inputs:** - \( A \): The first binary input. - \( B \): The second binary input. 2. **NOT Gate:** - A NOT gate inverts the input signal; if the input is 1, the output will be 0 and vice versa. 3. **XOR Gate:** - An XOR (Exclusive OR) gate outputs true or 1 only when the number of true inputs is odd. For two inputs, it outputs 1 when exactly one of the inputs is 1. ### Circuit Diagram: The diagram illustrates a circuit comprised of two main logic gates: 1. **NOT Gate Operation**: Not explicitly shown as an individual gate here, but let's assume it processes one of the inputs, say \( A \), before feeding into the XOR gate. 2. **XOR Gate Connections**: - The inputs \( A \) and \( B \) are connected to the XOR gate. - The output of the XOR gate then powers the bulb. ### Bulb Illumination (Output): The bulb will light up based on the output from the XOR gate. The XOR gate's output logic is as follows: - If \( A = 0 \) and \( B = 0 \), XOR Output is \( 0 \); the bulb does not light up. - If \( A = 0 \) and \( B = 1 \), XOR Output is \( 1 \); the bulb lights up. - If \( A = 1 \) and \( B = 0 \), XOR Output is \( 1 \); the bulb lights up. - If \( A = 1 \) and \( B = 1 \), XOR Output is \( 0 \); the bulb does not light up. ### Conclusion This simple circuit effectively demonstrates the role of XOR gates in digital logic. By understanding each gate's function, one can predict the circuit's output for various input states, highlighting fundamental principles in digital electronics.
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