integer to float How can represent any number from 0 to 127 as something between 0 and 1 ?
for example 64's equivalent would be 0.5

Lets look at numbers 1 to 128 rather than 0 to 127 because 0 to 127 can get confusing and the same formula will work for 0 to 127. We want to scale, or divide, each number by something so that the largest number is 1 and the smallest number is something greater than zero.  So lets look at our first idea. 
Call this number we want to divide by $x.$ Because we want our largest number, 128, to be equivalent to 1, we should get something like this: $\frac{128}{x}=1.$  Bring the $x$ to the other side and we will get $x=128.$  
So every number can be converted to a ''float'' by $\frac{number}{128}.$ 
