Transforming the product of sums expression into an equivalent sum-of-products expression

It is very vital topic that transforming the product of sums expression into an equivalent sum of products expression. It is a very simple and straightforward process.

 

  • Multiplying out the given expression

  • Do the simplification of the expression after multiplication.

 

 By the above mention process we can easily get the equivalent sum of products expression from product of sum expression.

And mind it it is very important process which we have to know because by transforming the product of sums expression into an equivalent sum of products expression we can simplify the digital logic circuit interns of reducing the number of literal or number of terms. 

Now take an example to see the process.LetY = (A+B+C^).(A+B^+C).(A^+B+C).(A^+B^+C^) and we have to convert this in sum of products expression.

   (A+B+C^).(A+B^+C).(A^+B+C).(A^+B^+C^)

=( AA+AB^+AC+BA+BB^+BC+C^A+C^B^+C^C).(A^A^+A^B^+A^C^+BA_+BB^+BC^+CA^+CB^+CC^)

= (A+BC +B^C^).(A^+BC^+CB^)

 = ABC^ +AB^C +A^BC +A^B^C^ …………………… Eqn 2.0

See that eqn 2.0 the three literal A, B, C are in arrange like sum of products expression.

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