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Fixed point numbers

Fixed-point representation
We must be able to use 2s complement binary numbers if we are to understand how to do floating-point numbers. The other thing we need to know is fixed-point representation of numbers. This is used because so far we have only represented whole numbers. There are times when we will want to represent fractions.

We could define a byte so that we can represent fractions! A simple way of achieving this is to fix the decimal point in a particular position. Let's set up our byte so we can do this. Some bits will represent whole numbers and some bits will represent fractions. Also notice that the decimal point isn't actually stored; it doesn't take up any of the bit positions. We 'know' where the decimal point is only because we know how we've defined each bit position.

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This system is known as the 'Fixed-point' system. How is it used? Here are some examples:

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