Final answer:
To get the minimum product of sums in a K-map, you group adjacent 1s and then apply DeMorgan's Theorem to the resulting SOP to get the POS expression. The correct answer is option C) Group adjacent 1s.
Step-by-step explanation:
The student is asking about obtaining the minimum product of sums (POS) in a Karnaugh map (K-map), which is a tool used in digital logic to simplify Boolean expressions. Here's a step-by-step explanation on how to get the minimum POS using a K-map:
- Identify the function you want to minimize and fill the K-map with 0s and 1s based on the truth table for the function.
- You should group adjacent 1s, which represents a simplified product term in the sum of products (SOP) form. For POS, you're interested in grouping the 0s instead; however, you usually convert these groups into 1s and then apply DeMorgan's Theorem to get the POS expression.
- To apply DeMorgan's Theorem, you first need the SOP of the inverted output, which you get by grouping 1s. Then you invert the entire expression to achieve the minimum POS.
- When grouping, always use the largest groups possible (containing 1, 2, 4, 8, etc., 1s or 0s) and make sure they are powers of 2. The groups should be as few as possible and can overlap if it results in fewer terms.
- Finally, for each group of 0s, you determine the sum term that is 0 for all the minterms in that group. The POS will be the product of these sum terms.
Based on this explanation, the correct answer to the question is C) Group adjacent 1s. You do this initially to identify the zeros that you need to group for the POS expression. The SOP form helps to get the complemented POS form, which is then inverted to achieve the required minimum POS form.