Question

You have a coord grid that is 96x96. what is the minimum number of bits that you will need to encode a coordinate in that space

Answer 1

One bit can code 2 type of possibilities. That mean 1 bit code 2^1 possibilities, 2 bits code 2^2 possibilities and X amount of bits will code 2^X possibilities. In this case, you need to code 96x96 possibilities= 9216 possibilities. To answer this question, you need to find out how much it will be in 2^X form.  The fast way  to solve it by dividing it with 32(2^5) until the value <32 then divide it with 2(2^1) till it become <1

9216/32= 288
288/32= 9 -->take the 1 extra to made it 8
8/2= 4
4/2= 2
2/2=1
1/2= 0.5

The number is divided by 32 two times and divided by 2 four times. Then the number of bits would be
5*2 + 1*4= 14 bits
The answer will be 14 bits since 14 bits will code 16384 possibilities