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Convert the following expressions to standard form of expression(i) F(w, x, y, z)= wxy + x’yz + yz

Question

Convert the following expressions to standard form of expression(i) F(w, x, y, z)= wxy + x’yz + yz

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Solution

The standard form of a Boolean expression is when it is simplified to the sum of minterms or product of maxterms. The given expression is F(w, x, y, z)= wxy + x’yz + yz.

To convert this to standard form, we need to express each term as a minterm. A minterm is a product of all the variables in the function, either in normal form or in complemented form.

  1. The first term wxy is already a minterm as it contains three variables.

  2. The second term x'yz is missing the variable w. We can add it in both its true and complemented form without changing the value of the term. So, x'yz becomes wx'yz + w'x'yz.

  3. The third term yz is missing the variables w and x. We can add them in both their true and complemented forms without changing the value of the term. So, yz becomes wxyz + wx'yz + w'xyz + w'x'yz.

So, the standard form of the given expression F(w, x, y, z) is F(w, x, y, z) = wxy + wx'yz + w'x'yz + wxyz + wx'yz + w'xyz + w'x'yz.

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