Final answer:
Maxterms covered by only one prime implicant in Boolean algebra are essential and can be identified through Karnaugh maps or tabular minimization methods. They are then listed in ascending decimal order to understand their significance in the simplified Boolean expression.
Step-by-step explanation:
To find the maxterms that are covered by only one prime implicant, we must first understand what a maxterm and a prime implicant are within the context of Boolean algebra, specifically in digital logic design and simplification. A maxterm is a logical sum (OR) of all variables in a function in either true or complemented form, such that when any one variable is true (1), the maxterm is false (0). A prime implicant is a product (AND) term in a minimized Boolean function that cannot be combined with another term to eliminate a variable. In the Karnaugh map or tabular minimization methods, a prime implicant 'covers' a maxterm if the corresponding minterm (the binary opposite of a maxterm) is a part of the implicant.
To determine which maxterms are covered by only one prime implicant, one would analyze the Karnaugh map or truth table after performing the simplification process. Maxterms covered only by a single prime implicant are essential to the final expression as they cannot be simplified further. These maxterms will remain in the Boolean expression after minimization.
Listing these maxterms in chronological order as comma-separated decimal numbers involves translating the binary representation of each maxterm to its decimal equivalent and then arranging them in ascending order.