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# 2. Binary points

On the last page, we saw that you could represent fractional numbers in binary.

-8 4 2 1 1/2 1/4 1/8 1/16
1 1 1 1 1 1 1 1

Just like with denary numbers, it's clear that there's a dividing point between the digits used to represent whole numbers, and digits used to represent fractions. The technical term for this is the radix point.

We call this the "decimal point" in denary. In binary, it's sensibly called the "binary point". You'd place it here:

If we use this scheme, then 1111 1111 represents

           -8 + 4 + 2 + 1 + 1/2 + 1/4 + 1/8 + 1/16
= -1 15/16 (approximately -1.937)

Because we have a fixed position for the binary point (between the 4th and 5th bits), we call this a fixed point binary scheme.

The binary point doesn't have to be between the 4th and 5th bits. You could move it to between the 1st and 2nd bits to allow for finer fractions. Or between the 7th and 8th bits if you want to allow more space for integers.

But notice the limited range a fixed point scheme provides. In the example above the largest positive number is 0111 1111 (there is no -8)

$$4 + 2 + 1 + \frac 1 2 + \frac 1 4 + \frac 1 8 + \frac 1 {16}$$

$$= +7 \frac {15} {16} \text { or approximately} +7.937$$

And so the range for this scheme is +7.937 to -1.937

Not very wide at all compared to the signed integer version of +127 to -128