https://file.aiquickdraw.com/mathbot/file/1734815144008bc8dfbid.jpg

The image contains logic circuits that need to be converted into Boolean expressions. I will break down each problem in the image and convert the logic gates into corresponding Boolean expressions step by step.

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### **Problem 2 (on the right side):**

1. **Inputs and Gates:**
   - Inputs: \( A, B, C \)
   - **AND gate** takes inputs \( A \) and \( B \), output = \( AB \).
   - **OR gate** takes the output of the AND gate (\( AB \)) and \( C \), output = \( (AB) + C \).

   **Boolean expression:** \((AB) + C\)

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### **Problem 3 (on the left side):**

1. **Inputs and Gates:**
   - Inputs: \( A, B, C, D \)
   - **First NOT gate:** Input \( D \), output = \( \overline{D} \).
   - **First AND gate:** Inputs \( \overline{D} \) and \( C \), output = \( \overline{D}C \).
   - **Second AND gate:** Inputs \( A \) and \( B \), output = \( AB \).
   - **OR gate:** Inputs \( \overline{D}C \) and \( AB \), output = \( (\overline{D}C) + (AB) \).

   **Boolean expression:** \((\overline{D}C) + (AB)\)

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Would you like detailed explanations of each step or more examples? 

### Related Questions:
1. What are the rules for simplifying Boolean expressions?
2. How can a truth table be created for \((\overline{D}C) + (AB)\)?
3. What are the differences between combinational and sequential logic circuits?
4. How can logic circuits be minimized using Karnaugh maps?
5. Can Boolean expressions be directly implemented into digital circuits?

### Tip:
Always identify the output of each gate step-by-step to prevent missing connections in logic circuit analysis.

Convert the logic gate circuits into Boolean expressions, writing Boolean sub-expressions next to each gate output in the diagram.

Learn how to convert complex logic circuits into Boolean expressions. This example breaks down circuits with AND, OR, and NOT gates into sub-expressions and final Boolean equations. Suitable for undergraduate students learning digital logic design.

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