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7. Write the Boolean expression in POS form for the truth table below. Plot O's on the K-Map and simplify the Boolean expression by determining prime implicants. Draw both the original and the simplified circuit. Xy| f 000|1 0011 0 10|1 0 11|0 1001 101|1 10 1 110 1 1

7. Write the Boolean expression in POS form for the truth table below. Plot O's on the K-Map and simplify the Boolean expression by determining prime implicants. Draw both the original and the simplified circuit. Xy| f 000|1 0011 0 10|1 0 11|0 1001 101|1 10 1 110 1 1

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
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**Problem Statement:** 7. Write the Boolean expression in POS form for the truth table below. Plot 0’s on the K-Map and simplify the Boolean expression by determining prime implicants. Draw both the original and the simplified circuit. **Truth Table:** | w | x | y | f | |---|---|---|---| | 0 | 0 | 0 | 1 | | 0 | 0 | 1 | 1 | | 0 | 1 | 0 | 1 | | 0 | 1 | 1 | 0 | | 1 | 0 | 0 | 1 | | 1 | 0 | 1 | 1 | | 1 | 1 | 0 | 1 | | 1 | 1 | 1 | 0 | **Explanation:** 1. **POS Form:** - The Product of Sums (POS) expression requires us to look at the rows where the output `f` is `0`. - From the truth table, `f` is `0` for the input combinations: (0 1 1), (1 1 1). 2. **Karnaugh Map (K-Map):** - Plot the `0` values on a K-Map to simplify the expression. - Identify and circle the groups of 1’s in the K-Map, which are used to derive the simplified expression. 3. **Determination of Prime Implicants:** - Find the largest possible groups of adjacent cells containing `0`. 4. **Circuit Drawings:** - Draw the original circuit based on the unsimplified Boolean expression. - Draw the simplified circuit based on the simplified expression obtained from the K-Map. By completing these steps, you can achieve both the original and simplified versions of the Boolean circuit.
Transcribed Image Text:**Problem Statement:** 7. Write the Boolean expression in POS form for the truth table below. Plot 0’s on the K-Map and simplify the Boolean expression by determining prime implicants. Draw both the original and the simplified circuit. **Truth Table:** | w | x | y | f | |---|---|---|---| | 0 | 0 | 0 | 1 | | 0 | 0 | 1 | 1 | | 0 | 1 | 0 | 1 | | 0 | 1 | 1 | 0 | | 1 | 0 | 0 | 1 | | 1 | 0 | 1 | 1 | | 1 | 1 | 0 | 1 | | 1 | 1 | 1 | 0 | **Explanation:** 1. **POS Form:** - The Product of Sums (POS) expression requires us to look at the rows where the output `f` is `0`. - From the truth table, `f` is `0` for the input combinations: (0 1 1), (1 1 1). 2. **Karnaugh Map (K-Map):** - Plot the `0` values on a K-Map to simplify the expression. - Identify and circle the groups of 1’s in the K-Map, which are used to derive the simplified expression. 3. **Determination of Prime Implicants:** - Find the largest possible groups of adjacent cells containing `0`. 4. **Circuit Drawings:** - Draw the original circuit based on the unsimplified Boolean expression. - Draw the simplified circuit based on the simplified expression obtained from the K-Map. By completing these steps, you can achieve both the original and simplified versions of the Boolean circuit.
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