Question

You have a coordinate grid that is 96 x 96. assuming that you encode the x and y coordinate as separate numbers, what is the minimum number of bits that you will need to encode a coordinate in that space?

Answer 1

One bits can code 0 or 1, which was 2 possibilities. Every bits can code $2^{x}$ possibilities with x is number of bits. The possibilities that need to be code is the coordinate. The possibilities should be: 96 x 96 = 9216 possibilities. 

The easy way to find the bits is by dividing the possibilities with 64 and every 64 is 5 bits( $2^{5}$=64) then 2 for 1 bits until it <1. Then the answer would be: 9216/64= 144/64= 2.25/ 2= 1.125/2= 0.5625

The number can be divided by 64 two times and divided by 2 two times, make it 10+2 bits. = 12 bits