After reading the homework 6 pdf, it seems it ask us to do the adder digit by digit? Can we construct the 64bit adder by connect 16 4bit adders together using a for loop?

You should be assembling bigger adders in a hierarchical fashion. So, for example, to build a 16-bit adder, use 4 4-bit adders. To build a 64-bit adder, use 4 16-bit adders. It’s this hierarchy that provides us with the speed. In fact, everyone should study why this configuration is preferred over stringing together 64 1-bit adders, 16 4-bit adders, etc. Appendix B.6 uses the prefix “super,” e.g., super propagate, super generate. The textbook coverage is fairly thorough.

How will the program receive its input, and did you have any specific test cases in mind (like test_matrix.dat for assignment 1)?

I should have specified. Entering 64 bits would be a little tedious. You should supply your input in hexadecimal. So you should have something similar to this:

long hex_val;
printf("Please enter a (hex) value: ");
scanf("%lx", &hex_val);
printf("%lx", hex_val);

You can even add them to check your answer.

Step 7 in the pdf says sum_i = a_i +b_i +c_i, but the top of the pdf has c_{i-1} instead of c_i. Isn’t c_{i-1} correct?

Step 7 builds on step 6, step 8 builds on step 7, etc. You calculate them based on the incoming c_x value which is why those indices are changing.

In step 5 (and similarly in 6) where it says k = j mod 4, should this be a division instead of a mod? I’m thinking that j goes from 0 to 15, so sections will begin at multiples of 4, so taking j mod 4 will always give you k=0 and therefore only give you sc_0 as your carry-in for each of the sections.

Yes, you are correct! I will adjust the PDF accordingly.

Is this just going to be for unsigned numbers, or will negative numbers be added too?

Unsigned values are fine and we won’t be testing negative values, overflows, or anything like that.

Are we required to also express the hexadecimal values as decimals like you did? Or is that simply for clarity? Also are we required to then convert the binary sum back into hex and decimal? I didn’t see that specified anywhere on the assignment.

When sample output is supplied, it’s usually best to try and mimic it as closely as possible. That said, it’s actually the binary representation that is rather unusual. Packing those bits into, say, an unsigned long is much more natural and then you will be able to utilize the printf() function to print the value in any format you wish. See this stackoverflow answer for help with dealing with binary values. Once the bits are in a well-supported type the conversions become trivial.