When two or more product terms are summed by Boolean addition, the resulting expression is sum-of-products (SOP). Eg:-
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| Sum-of-Product (SOP) |
The expression above has a domain made up of the variables A,B,C and D. However, notice that the complete set of variables is not represented in the first two terms of the expressions.
A standard SOP expression is one in which all the variables in the domain appear in each product term in the expression. Standard SOP expressions are important in constructing truth tables and in Karnaugh Map simplification method.
Any nonstandard SOP expression can be converted to the standard form using Boolean algebra (Rule 6).
Step 1.
Multiply each nonstandard product term by a term made up of the sum of a missing variable and its complement.
Step2.
Repeat step 1 until all resulting product terms contain all variables in the domain in either complemented or uncomplemented form. In converting a product term to standard form, the number of product terms is doubled for each missing variable.
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| Convert Boolean expression into standard SOP form. Refer to Example 4-13, page 202 |
Missing variables in nonstandard form =2
Number of product terms in nonstandard form =3
After converting to standard SOP form = 3 + (2x2) =7
Thus, number of product terms in standard form = 7
Reference:-
Digital Fundamentals, by Floyd ( page 200-202)
