Final answer:
A boolean equation in product-of-sums canonical form is the product (AND) of sum terms, where each term corresponds to a specific condition where the function is false. Each variable in a sum term is complemented if it equals 0 and non-complemented if it equals 1 in the truth table.
Step-by-step explanation:
To write a boolean equation in product-of-sums (POS) canonical form, you need to first understand that the POS form is a logical expression where the output is the product (AND) of multiple sums (ORs) of the variables or their complements. The canonical form means it should include all variables in each term, either in true or complemented form.
Assuming we are given a truth table or a function to convert, the process involves the following steps:
- Determine the rows of the truth table where the output is 0.
- Write a sum term for each of these rows with the variable complemented if it is 0 in the row and not complemented if it is 1.
- Take the product (AND) of all these sum terms to complete the equation.
For example, given a function F with inputs A, B, and C, if F is only false for inputs (0,1,1) and (1,0,0), the POS canonical form would be:
(A + B' + C') (A' + B + C)
This means that the function F is true except for the conditions represented in the product terms.
Remember that ' represents the complement or NOT operation in Boolean algebra. The above example explicitly shows how each product term in the canonical POS form corresponds to a specific configuration where the function is 0, accounting for each variable.