1. Draw the K-Map and give the minimized result from the following Boolean function: Z = f(A,B.C) = AB C + AB + ABC + AC
1. Draw the K-Map and give the minimized result from the following Boolean function: Z = f(A,B.C) = AB C + AB + ABC + AC
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![**Problem 1: Drawing and Minimizing a K-Map**
**Objective:** Draw the Karnaugh Map (K-Map) and provide the minimized result for the given Boolean function.
**Boolean Function:**
\[ Z = f(A, B, C) = \overline{A} \overline{B} \overline{C} + \overline{A} B + \overline{A} BC + AC \]
**Steps to Solve:**
1. **Identify Variables:** The function involves three variables: A, B, and C.
2. **Construct the K-Map:**
- A 3-variable K-Map will have 2^3 = 8 cells.
- Label the axis with all combinations of B and C, and consider each as a row based on A.
3. **Fill the K-Map:**
- Place a '1' in cells corresponding to minterms in the given function.
- For example, place '1' for terms \(\overline{A} \overline{B} \overline{C}\), \(\overline{A} B\), \(\overline{A} BC\), and \(AC\).
4. **Group the 1s:**
- Group the 1s in powers of two (e.g., groups of 1, 2, or 4) to simplify the function.
- Aim for covering all 1s with the least number of groups.
5. **Derive the Simplified Expression:**
- Use the groups to write the simplified Boolean expression.
- Each group corresponds to a simplified term.
**Note:** The completion of this process will yield the minimized Boolean expression. Understanding K-Maps helps in reducing complex logic circuits more efficiently.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe4d51557-a52e-4953-889e-69e3a0700485%2F691b6763-1fcc-4d59-b5f6-7d08ef5ff15b%2Fcp1493q_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem 1: Drawing and Minimizing a K-Map**
**Objective:** Draw the Karnaugh Map (K-Map) and provide the minimized result for the given Boolean function.
**Boolean Function:**
\[ Z = f(A, B, C) = \overline{A} \overline{B} \overline{C} + \overline{A} B + \overline{A} BC + AC \]
**Steps to Solve:**
1. **Identify Variables:** The function involves three variables: A, B, and C.
2. **Construct the K-Map:**
- A 3-variable K-Map will have 2^3 = 8 cells.
- Label the axis with all combinations of B and C, and consider each as a row based on A.
3. **Fill the K-Map:**
- Place a '1' in cells corresponding to minterms in the given function.
- For example, place '1' for terms \(\overline{A} \overline{B} \overline{C}\), \(\overline{A} B\), \(\overline{A} BC\), and \(AC\).
4. **Group the 1s:**
- Group the 1s in powers of two (e.g., groups of 1, 2, or 4) to simplify the function.
- Aim for covering all 1s with the least number of groups.
5. **Derive the Simplified Expression:**
- Use the groups to write the simplified Boolean expression.
- Each group corresponds to a simplified term.
**Note:** The completion of this process will yield the minimized Boolean expression. Understanding K-Maps helps in reducing complex logic circuits more efficiently.
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