Code_ The Hidden Language of Computer Hardware and Software - Charles Petzold [140]
The most interesting development for UNIX in recent years has been the Free Software Foundation (FSF) and the GNU project, both founded by Richard Stallman. GNU (pronounced not like the animal but instead with a distinct G at the beginning) stands for "GNU's Not UNIX," which, of course, it's not. Instead, GNU is intended to be compatible with UNIX but distributed in a manner that prevents the software from becoming proprietary. The GNU project has resulted in many UNIX-compatible utilities and tools, and also Linux, which is the core (or kernel) of a UNIX-compatible operating system. Written largely by Linus Torvalds of Finland, Linux has become quite popular in recent years.
The most significant trend in operating systems since the mid-1980s, however, has been the development of large and sophisticated systems, such as the Apple Macintosh and Microsoft Windows, that incorporate graphics and a visually rich video display intended to make applications easier to use. I'll describe this trend in the last chapter of this book.
Chapter 23. Fixed Point, Floating Point
Numbers are numbers, and in most of our daily lives we drift casually between whole numbers, fractions, and percentages. We buy half a carton of eggs and pay 8 ¼ percent sales tax with money earned getting time-and-a-half for working 2 ¾ hours overtime. Most people are fairly comfortable—if not necessarily proficient—with numbers such as these. We can even hear a statistic like "the average American house-hold has 2.6 people" without gasping in horror at the widespread mutilation that must have occurred to achieve this.
Yet this interchange between whole numbers and fractions isn't so casual when it comes to computer memory. Yes, everything is stored in computers in the form of bits, which means that everything is stored as binary numbers. But some kinds of numbers are definitely easier to express in terms of bits than others.
We began using bits to represent what mathematicians call the positive whole numbers and what computer programmers call the positive integers. We've also seen how two's complements allow us to represent negative integers in a way that eases the addition of positive and negative numbers. The table on the following page shows the range of positive integers and two's-complement integers for 8, 16, and 32 bits of storage.
Number of Bits
Range of Positive Integers
Range of Two's-Complement Integers
8
0 through 255
–128 through 127
16
0 through 65,535
–32,768 through 32,767
32
0 through 4,294,967,295
–2,147,483,648 through 2,147,483,647
But that's where we stopped. Beyond whole numbers, mathematicians also define rational numbers as those numbers that can be represented as a ratio of two whole numbers. This ratio is also referred to as a fraction. For example, ¾ is a rational number because it's the ratio of 3 and 4. We can also write this number in decimal fraction, or just decimal, form: 0.75. When we write it as a decimal, it really indicates a fraction, in this case
You'll recall from Chapter 7 that in a decimal number system, digits to the left of the decimal point are multiples of integral powers of ten. Similarly, digits to the right of the decimal point are multiples of negative powers of ten. In Chapter 7, I used the example 42,705.684, showing first that it's equal to
4 x 10,000 +
2 x 1000 +
7 x 100 +
0 x 10 +
5 x 1 +
6 ÷ 10 +
8 ÷ 100 +
4 ÷ 1000
Notice the division signs. Then I showed how you can write this sequence without any division:
4 x 10,000 +
2 x 1000 +
7 x 100 +
0 x 10 +
5 x 1 +
6 x 0.1 +
8 x 0.01 +
4 x 0.001
And finally here's the number using