The expression for the truth table given below in POS form is given by :
Question
The expression for the truth table given below in POS form is given by :
Solution
To find the expression for the truth table given below in POS form, we need to follow these steps:
- Identify the rows in the truth table where the output is 0.
- For each of these rows, create a product term (AND) that includes all the input variables, with each variable negated if its corresponding input in that row is 0.
- Combine all the product terms using OR operations.
Let's take an example truth table:
| A | B | C | Output |
|---|---|---|---|
| 0 | 0 | 0 | 1 |
| 0 | 0 | 1 | 0 |
| 0 | 1 | 0 | 1 |
| 0 | 1 | 1 | 0 |
| 1 | 0 | 0 | 1 |
| 1 | 0 | 1 | 1 |
| 1 | 1 | 0 | 0 |
| 1 | 1 | 1 | 1 |
Step 1: Identify the rows where the output is 0. In this case, it is rows 2, 4, and 6.
Step 2: Create product terms for each of these rows:
- For row 2: (A')(B')(C)
- For row 4: (A')(B)(C')
- For row 6: (A)(B)(C')
Step 3: Combine the product terms using OR operations: Expression = (A')(B')(C) + (A')(B)(C') + (A)(B)(C')
So, the expression for the given truth table in POS form is (A')(B')(C) + (A')(B)(C') + (A)(B)(C').
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