how can the Boolean expression be given marked at each stage inside the 16 row truth table ?

how can the Boolean expression of this table be given marked at each stage marked with a box ? 

The way your truth table is numbered is a bit confusing but this is what I would do. I see you've done the first step which is put the logic equation after each gate. So you need to label the columns with the same equations. For instance column 3 would be /A and so on.Then you should be able to write it out as Max explains in the column he just posted.
https://www.eeweb.com/profile/max-maxfield/ar...ic-gates-truth-tables-and-karnaugh-maps-oh-my

Hi there -- here's the deal -- I know how hard it can be to wrap your brain around this stuff when you are starting out, but you can't expect the folks on this site to do all the work for you -- now is the time for you to make a concentrated effort to memorize the truth tables for the NOT, AND, and OR functions and to really focus on understanding how they work when you connect them together.

With regard to your question, I've just whipped up a detailed step-by-step guide as follows:

http://www.clivemaxfield.com/area51/do-not-delete/max-0209-followup.pdfWhat you have to do is not just hand this in as your own work, but to to study it and work hard to understand what I did and how I did it. Once you understand this, you can apply it to any similar problem. Good Luck!

On the one hand I'm getting a little "frayed" by all this -- on the other hand I (vaguely) recall what it was like not to know it -- in the case of my follow-up comment/document below, I'm hoping the light bulb will turn on... fingers crossed

Also check out this column about using a 3-input (8:1) multiplexer to implement a 4-input function.