comparator

Hello all, i am trying to get a comparator working with Hysteresis. A 500mV is the target between Vlth 2v and Vhth 2v5. Can somebody please help me with the Hysteresis part with an explanation for the attached LTSpice simulation.

How to make a full bit (2bit) comparator circuit using ONLY nand gates. I was able to do a 1bit comparator using only NAND gates, but how about for 2 bit, 4 bit? Wouldnt it be really large. I'm not sure if my class expects us to draw this out. we can't even use xor gates or inverters. i have...