You could code the whole game sequence in only 22 bits.

First bit to mark whether X or O starts, then 4 bits for the placement of the first symbol (9 empty squares numbered 0-8 counting from top left), then only 3 bits for the second one (one square is already taken so there are only 8 possible positions left), etc. which gives us 4+3+3+3+3+2+2+1 = 21 bits for the 8 moves before there is only one unfilled square left.