You could only use 2 gates, that was specified in the question. Who ever wrote the previous proof is using the incorrect truth table. This is the correct diagram and table as below and produces the correct output.
In boolean algebraic terms the expression is as below. You don't need to know how to apply DeMorgan's theorems to the Sum Of Products. You simply had to know the truth table for an OR gate, and chuck in a NOT gate for the 2 inputs that needed to be different.
B' + A
For the PS2 Mouse question it required you to know that each chunk on 7 bits made up a byte, why? because the first bit was the header information separating each byte(and the nature of each byte) they didn't show it because it would have confused people way too much and it wasn't really relevant to the question, you just had to apply your knowledge to the 7 bits presented in the 3 bytes.(
pg473 2012 davis textbook). They were even so kind to choose a question that had an error checking bit which was always zero, hence if you lost your place and the bit wasn't zero, it would be obvious.
The first byte gave gave you the fact the the left click was pressed, the direction the mouse moved on the x plane was negative and the direction in the y plane was positive. The second byte gave you the amount the mouse moved in the x plane which was 72 in the negative. The third byte gave you the amount in the y plane which was positive 224.
So in summary the answer to the question was simply an interpretation of the binary based on the table given. i.e. the answer was;
Byte 1 - Left click pressed, x direction negative, y direction positive
Byte 2 - 72 in the x direction
Byte 3 - 224 in the y direction
Now apply the signs to each of the directions and graph it. Giving you the point (-72, 224). You had to either graph it and indicate the left click or write what each of the bytes gave for full marks, you did not have to do both.