Isn't 7493 a counter? What does a counter have to do with the above design?
Unless this circuit does someting standard, which I don't see at the time, you could use 2 IC's to build it. One 7486 for the 4 XOR's and one 7400 for the AND's.
It would be nice if someone would recomend a series other than 74XX too.
First of all, let me correct my previous post. I see now that the circuit is a 2-bit counter, but not the type of the 7493, which is a flip-flop counter. It is a carry-out prediction, no-carry-in counter.
But what does the OP want to do with this? Do you want a truth table? A way to build it on a board? A description of its function? Please be more descriptive.