Question

How to convert non standard pos (B+C).(A+B'+c')to standard pos form

Answer 1

To convert the non-standard POS (B+C).(A+B'+C') to standard POS, you expand it, eliminate null terms, and include all variables in all terms, resulting in (A+B+C)(A+B+C')(A+B'+C)(A+B'+C').

Step-by-step explanation:

To convert a non-standard Product of Sums (POS) expression to standard POS form, you can expand the expression and combine like terms to ensure every term includes all variables present in the expression. The given non-standard POS expression is (B+C).(A+B'+C'). In standard POS form, each term of the expression must include all unique variables either in straight or complemented form.

Here's how we can convert the given expression to standard POS form:

1. Distribute the first term over the second term: (B+C).(A+B'+C') = B(A+B'+C') + C(A+B'+C').
2. Apply the distribution for each term: B(A+B'+C') = BA + BB' + BC', and C(A+B'+C') = CA + CB' + CC'.
3. Since B and B' are complements, BB' = 0, and similarly CC' = 0. Therefore, reduce the expression by eliminating these terms.
4. The reduced expression will then be BA + BC' + CA + CB'.
5. In standard POS form, we must include all variables in each term. As we do not have all the variables in each term, we add the missing ones in the form of X+X' which equals 1.
6. After including all variables, the standard POS form becomes (A+B+C)(A+B+C')(A+B'+C)(A+B'+C').

This is the expression in standard POS form where each term contains all variables in either true or complemented form.