How do you fill this circuit-table correctly (digital comparator)?
Based on the facts you mentioned, we are given an module of inputs A,B,C and output Y such that the output Y is high if A>B we want to build a bigger module that compares 3-bit such that if A bit string is bigger than B the output will be 1.

My approach for solving this problem was as the following 


In this combination if A > B or A==B the first OR gate output will be 1 while if A &lt; B the first OR gate output will be 0, the OR output is connected to the second comparator C_i input, so basicly i`m using the C_i input as if it was a confimation that the previous A was not smaller than B. 

So as long as the input C for any of those single bit comparators is 1 the comparator output will be 1 or 0 based on which is bigger A or B, while if this input C is 0, the comparator output will always be 0!

Lets do some test cases

A=010
B=001


The first comparator [The one of the LEFT] has inputs A=0, B=0, C=1 the output of this comparator is 0 since A2 is not bigger than B2 while the XNOR gate [XOR followed by a not gate] output is 1 since A is equal to B this means that the second comparator will work and we still not sure if A is bigger than B or not

The second comparator now has inputs A=1, B=0, C=1 the output of this comparator is now 1 since A3 > B3 both the inputs of the second OR gate are 1

The third comparator now has inputs A=0, B=1, C=1 the output of this comparator is now 0 since A[0]

The final result is taken by a big OR gate that checks if any of the comparators output was equal to one

Now your back to filling your table assuming the same values of A and B your table should look like this



You can play around the values of A and B and check out the values of C_i using this simple Python Script

I hope this answer is not confusing and please if you think i am missing anything let me know 

EDITED


  What is meant by "big comparator output"?


I mean the whole circuit, in the image above its the 3-bit comparator which is made from 3x 1bit comparators and its output is the last or gate output




  what is C(i-1) in your description?


based on what you mentioned above 


  Each of these 1-bit modules have the inputs A_i, B_i and C_i-1


So in my case its the carry input for any of the comparators which should be 1 if A > B or A=B
 

Seems like your question requires comparing the numbers from right to left [based on the less significant digit] while my answer compares the numbers from left to right [based on the last significant digit] which means that this answer is not what you are looking for.

If this answer is not the proper answer for your question please let me know in the comments, I`ll delete it asap