Floating Point/Floating-Point Numbers
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This page is going to introduce floating point numbers, and explain some key terminology.
Terminology[edit | edit source]
- base
- The base of a floating-point number is the number to which the exponent is applied. In our decimal counting system, the base is usually 10. In a binary system, however, the base is usually 2. In the following number: , 10 is the base.
- precision
- The precision of a number is the amount of places available after the decimal point. In the scientific-notation number: , the precision is 4 because there are 4 digits after the decimal point.
- significand
- The significand is the value of the non-exponent part of the number. In the number , 1.2345 is the significand. This is also called the mantissa.
- exponent
- The exponent is the number to which the base is raised. In the number , 6 is the exponent.
Where: m is the significand b is the base e is the exponent |
Biasing[edit | edit source]
In computer science, a number is called biased, if it has associated with it a certain additive offset value. For instance, if we have a 3 bit number (from 0 to 111_{2}, which is 7 in decimal), we can define a bias of 4, so that every number value has 4 subtracted from it to provide the final value. Here are some examples:
unbiased number | biased number |
---|---|
0 | 0 - 4 = -4 |
7 | 7 -4 = 3 |
This means that our number, now that it has been biased can go from -4 to 3. Biasing is only one of many methods for allowing binary values to express negative values.
Variables[edit | edit source]
There are a number of variables that we will use throughout this book, and we are going to explain a few of them here:
- b
- b is the base number.
- e
- We will use the letter e to represent the number of bits in an exponent. This means that the exponent can take all integer values from 0 to .
- p
- This is the precision value of the significand.