**Truth Table and Boolean Expression**Write a Boolean Product of Sum (POS) expression for this truth table and then simplify that expression as much as possible.| A | B | C | Output ||-------|-------|-------|--------|| 0 | 0 | 0 | 0 || 0 | 0 | 1 | 0 || 0 | 1 | 0 | 0 || 0 | 1 | 1 | 1 || 1 | 0 | 0 | 1 || 1 | 0 | 1 | 1 || 1 | 1 | 0 | 0 || 1 | 1 | 1 | 0 |**Explanation:**- A truth table is a mathematical table used to determine the output of a logic circuit based on all possible combinations of inputs. In this table, the inputs are represented by columns A, B, and C, and the output is listed under the "Output" column.- The goal is to write a Boolean expression in Product of Sum (POS) form based on the given truth table, and simplify it.**POS Expression and Simplification:**1. **Identify Rows with Output = 0** The logic for POS is constructed from rows where the output is 0. These rows are: - (A=0, B=0, C=0) - (A=0, B=0, C=1) - (A=0, B=1, C=0) - (A=1, B=1, C=0) - (A=1, B=1, C=1)2. **Write the Sum Terms:** For each row, write the sum term by inverting the inputs: - (A=0, B=0, C=0): \(A + B + C\) - (A=0, B=0, C=1): \(A + B + \overline{C}\)

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Answered: a. Write a Boolean Product of Sum (POS)…

a. Write a Boolean Product of Sum (POS) expression for this truth table b. then simplify that expression as much as possible. A B Output 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

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Chapter1: Introduction

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Question

**Truth Table and Boolean Expression**

Write a Boolean Product of Sum (POS) expression for this truth table and then simplify that expression as much as possible.

| A | B | C | Output |
|-------|-------|-------|--------|
| 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 1 | 1 | 1 |
| 1 | 0 | 0 | 1 |
| 1 | 0 | 1 | 1 |
| 1 | 1 | 0 | 0 |
| 1 | 1 | 1 | 0 |

**Explanation:**

- A truth table is a mathematical table used to determine the output of a logic circuit based on all possible combinations of inputs. In this table, the inputs are represented by columns A, B, and C, and the output is listed under the "Output" column.
- The goal is to write a Boolean expression in Product of Sum (POS) form based on the given truth table, and simplify it.

**POS Expression and Simplification:**

1. **Identify Rows with Output = 0**

The logic for POS is constructed from rows where the output is 0. These rows are:

- (A=0, B=0, C=0)
- (A=0, B=0, C=1)
- (A=0, B=1, C=0)
- (A=1, B=1, C=0)
- (A=1, B=1, C=1)

2. **Write the Sum Terms:**

For each row, write the sum term by inverting the inputs:

- (A=0, B=0, C=0): \(A + B + C\)
- (A=0, B=0, C=1): \(A + B + \overline{C}\)

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