4. Using what you just learned about Boolean Algebra, build a circuit in Multimedia that will satisfy the following Boolean equation: X=A•B•C Draw your circuit below: Develop a truth table for your circuit below:

Electric Motor Control
10th Edition
ISBN:9781133702818
Author:Herman
Publisher:Herman
Chapter22: Sequence Control
Section: Chapter Questions
Problem 6SQ: Draw a symbol for a solid-state logic element AND.
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### Understanding Boolean Algebra and Circuit Design

**The AND gate operation can also be expressed by a Boolean Algebra equation. For the two-input AND gate you just worked with, the equation is:**

\[ X = A \cdot B \]

**4. Using what you just learned about Boolean Algebra, build a circuit in Multimedia that will satisfy the following Boolean equation:**

\[ X = A \cdot B \cdot C \]

**Draw your circuit below:**

*Here, you are expected to draw a circuit diagram that represents the Boolean equation \( X = A \cdot B \cdot C \). This would typically involve three inputs (A, B, C) going into AND gates whose output is X.*

**Develop a truth table for your circuit below:**

*In this section, you are to create a truth table that reflects all possible inputs (A, B, C) and the corresponding output (X) for the Boolean equation \( X = A \cdot B \cdot C \).*

---

### Guide to Drawing the Circuit and Developing a Truth Table

**Circuit Design:**
1. **Elements Required:**
   - Three input variables: A, B, and C.
   - AND gates.

2. **Steps:**
   - Connect input A and B to the first AND gate.
   - The output of the first AND gate will join with input C at the second AND gate.
   - The final output from the second AND gate will be your X.

**Truth Table:**
A truth table for the given equation \( X = A \cdot B \cdot C \) helps in predicting the output for all possible combinations of inputs A, B, and C.

| A | B | C | X |
|---|---|---|---|
| 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 1 | 1 | 0 |
| 1 | 0 | 0 | 0 |
| 1 | 0 | 1 | 0 |
| 1 | 1 | 0 | 0 |
| 1 | 1 | 1 | 1 |

In this table, '0' represents a LOW state or FALSE condition, and '1' represents a HIGH state or TRUE condition.
Transcribed Image Text:--- ### Understanding Boolean Algebra and Circuit Design **The AND gate operation can also be expressed by a Boolean Algebra equation. For the two-input AND gate you just worked with, the equation is:** \[ X = A \cdot B \] **4. Using what you just learned about Boolean Algebra, build a circuit in Multimedia that will satisfy the following Boolean equation:** \[ X = A \cdot B \cdot C \] **Draw your circuit below:** *Here, you are expected to draw a circuit diagram that represents the Boolean equation \( X = A \cdot B \cdot C \). This would typically involve three inputs (A, B, C) going into AND gates whose output is X.* **Develop a truth table for your circuit below:** *In this section, you are to create a truth table that reflects all possible inputs (A, B, C) and the corresponding output (X) for the Boolean equation \( X = A \cdot B \cdot C \).* --- ### Guide to Drawing the Circuit and Developing a Truth Table **Circuit Design:** 1. **Elements Required:** - Three input variables: A, B, and C. - AND gates. 2. **Steps:** - Connect input A and B to the first AND gate. - The output of the first AND gate will join with input C at the second AND gate. - The final output from the second AND gate will be your X. **Truth Table:** A truth table for the given equation \( X = A \cdot B \cdot C \) helps in predicting the output for all possible combinations of inputs A, B, and C. | A | B | C | X | |---|---|---|---| | 0 | 0 | 0 | 0 | | 0 | 0 | 1 | 0 | | 0 | 1 | 0 | 0 | | 0 | 1 | 1 | 0 | | 1 | 0 | 0 | 0 | | 1 | 0 | 1 | 0 | | 1 | 1 | 0 | 0 | | 1 | 1 | 1 | 1 | In this table, '0' represents a LOW state or FALSE condition, and '1' represents a HIGH state or TRUE condition.
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