Good Afternoon,

I'm new to assembly and I have to do a small MIPS program. The details of are:
You can simulate the algorithm for 16 bits integers, not 32 bits integers. More specifically, we have two integers of 16 bits as input, add those two integers and get a 32 bits integer.
By this way, you do not need to use two registers to store 64 bits integers and deal with shifting between two difference registers.

I really appreciate your help, in how to start the program.

Thank you

Well, if i understoor correctly you have two integers that are of 16 bits and you need to add those into a new integer of 32 bits.
Ok, what you can do, it's not every assembly register that are of 32 bits.
EAX, EBX, ECX for example are 32 bits register(DWORD)
AX, BX, CX are 16 bits register(WORD)
AL, AH are 8 bits register(BYTE)

You can use one of this > 32 bits registers to do whatever you need