Designing a 2 bit magnitude comparator
Lets examine what a comparator should do:


  If A1 is greater than B1 then output 1, otherwise continue.
  If A0 is greater than B0 then output 1, otherwise output 0.


So now we can break this into parts.


  If A1 is greater than B1


This one you already have.

\$X_1 = A_1 \overline{B_1}\$


  If A0 is greater than B0


Second verse, same as the first.

\$X_0 = A_0 \overline{B_0}\$


  ... then output 1, otherwise continue. ...  then output 1, otherwise output 0.


Let's put up a truth table for this.

X1 X0  O
1  X   1
0  1   1
0  0   0


\$O = X_1 + X_0\$

So altogether we have:

\$O = A_1 \overline{B_1} + A_0 \overline{B_0}\$

And you're done.