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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 :

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Solution

To find the expression for the truth table given below in POS form, we need to follow these steps:

  1. Identify the rows in the truth table where the output is 0.
  2. 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.
  3. 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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