Final answer:
The function f(A,B,C,D) = Pm(0, 1, 2, 7, 8, 9, 10, 15) can be written as a Boolean expression in both canonical minterm and maxterm forms by representing the specific minterms and maxterms corresponding to the given numbers. Therefore correct option is (a) Write this as a Boolean expression in canonical minterm form.
Step-by-step explanation:
(a) To write the given function f(A,B,C,D) = Pm(0, 1, 2, 7, 8, 9, 10, 15) as a Boolean expression in canonical minterm form, we will express the function using individual minterms that correspond to the given decimal numbers. Each minterm represents a unique combination of the variables A, B, C, and D, where the value is 1.
Here, 'Pm' denotes the set of minterms. The minterm for a decimal 0 would include all variables being false, i.e., ¬ A ∧ ¬ B ∧ ¬ C ∧ ¬ D. As such, the complete Boolean expression would include all of the minterms for the specified indices.
(b) To rewrite the given function in canonical maxterm form, we use the complement of the indices that were not mentioned in the minterm representation, representing the combinations of A, B, C, and D which make the function 0. These are called maxterms, and each maxterm represents a unique combination of variables where the value is 0.
(c) Writing the complement of f in "little m" notation would involve creating a minterm expression for the complement function, which includes all minterms that were not included in the original function f.
(d) Writing the complement of f in "big M" notation as a canonical maxterm expression would include all the maxterms that are not included in the complement of the minterm expression from (c).
Therefore correct option is (a) Write this as a Boolean expression in canonical minterm form.