Getting the number of Saturdays and Sundays in a month

I am trying to get the number of Saturdays and Sundays for a given month represented by an end_date and a start date.

I have been trying to understand the algorithm in the SO question here . I have understood the matrix they have created but I don't get the algorithm that is being used, plus the thing is just the opposite of what is needed, and this thing is pretty new to me, mostly I do normal select, insert, update and joins in mysql.

It would be helpful to get some ideas on this issue.