### A good answer might be:

`28 = 256`

# Limited Precision

This is an easy question. If `N` bits are used, then only `2N` things can be represented, no matter what type of things they are. Eight bits can represent 256 positive integers (unsigned binary), 256 positive and negative integers (two's complement), 256 fractional numbers (our fixed point method), and so on. Here is a number line showing the 256 values that can be represented with this fixed notation:

The smallest value is zero (`00000000`); the largest value is 15.9375 (`11111111`). The smallest non-zero value is 0.0625. Every represented value is a multiple of 0.0625. Another way to think of fixed point notation is that the eight bits represent an integer from 0 to 255. The integer is a multiplier of the value 0.0625.

The range between any two integers is divided into 16 numbers (because 16*0.0625 = 1.0). This is not very many divisions. There are big gaps between represented numbers.

The important point of all this is that on the number line from zero to eight not all real numbers can be represented. This is called a limit in precision. Floating point representation has the same problem.

### QUESTION 10:

(Calculus Review: ) How many real numbers lie between 0.0 and 0.0625?