Given f(w, x, y, z) = ∑m (0, 1, 2, 3, 7, 8, 10) + ∑d (5, 6, 11, 15), where d represents the don’t-care condition in Karnaugh maps. Which of the following is a minimum product-of-sums (POS) form of f(w, x, y, z)?This question was previously asked inGATE CS 2017 Official Paper: Shift 2Attempt OnlineView all GATE CS Papers >f = (w̅  + z̅ )(x̅  + z)f = (w̅ + z)(x + z)f = (w + z)(x̅ + z)f = (w + z̅ )(x̅ + z)

This question is about digital logic design and Karnaugh maps. The function f(w, x, y, z) is given in the sum-of-minterms form, with some don't-care conditions. The task is to find the minimum product-of-sums (POS) form of the function.

Here are the steps to solve this problem:

1. First, we need to draw a 4-variable Karnaugh map (K-map). The variables w, x, y, z will represent the rows and columns of the K-map.

2. Next, we fill in the K-map with the given minterms (0, 1, 2, 3, 7, 8, 10) and don't-care conditions (5, 6, 11, 15).

3. Then, we need to group the 1s in the K-map. In a POS expression, we are looking for the maximum number of 0s that can be grouped together. However, we can also group the 1s and then apply DeMorgan's law to get the POS expression.

4. After grouping, we write down the POS expression for each group. Remember that for a POS expression, we write the variables that do not change within a group. If a variable is in its normal form, it is written as it is, and if it is in its complemented form, it is written with a bar over it.

5. Finally, we apply DeMorgan's law to the obtained expression to get the minimum POS form.

Without the actual Karnaugh map, it's impossible to give the correct answer from the options you provided. However, the process I described will help you find the correct answer.