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copied!<p>Great questions. K&R was written back in the days when there was a lot less to know about computers, and so programmers knew a lot more about the hardware. Every programmer <em>ought</em> to be familiar with this stuff, but (understandably) many beginning programmers aren't.</p> <p>At Carnegie Mellon University they developed an entire course to fill in this gap in knowledge, which I was a TA for. I recommend the textbook for that class: "Computer Systems: A Programmer's Perspective" <a href="http://amzn.com/013034074X/" rel="noreferrer">http://amzn.com/013034074X/</a></p> <p>The answers to your questions are longer than can really be covered here, but I'll give you some brief pointers for your own research.</p> <p>Basically, computers store all information--whether in memory (RAM) or on disk--in binary, a base-2 number system (as opposed to decimal, which is base 10). One binary digit is called a bit. Computers tend to work with memory in 8-bit chunks called bytes.</p> <p>A char in C is one byte. An int is typically four bytes (although it can be different on different machines). So a char can hold only 256 possible values, 2^8. An int can hold 2^32 different values.</p> <p>For more, definitely read the book, or read a few Wikipedia pages:</p> <ul> <li><a href="http://en.wikipedia.org/wiki/Binary_numeral_system" rel="noreferrer">http://en.wikipedia.org/wiki/Binary_numeral_system</a></li> <li><a href="http://en.wikipedia.org/wiki/Twos_complement" rel="noreferrer">http://en.wikipedia.org/wiki/Twos_complement</a></li> </ul> <p>Best of luck!</p> <p><strong>UPDATE</strong> with info on modular arithmetic as requested:</p> <p>First, read up on modular arithmetic: <a href="http://en.wikipedia.org/wiki/Modular_arithmetic" rel="noreferrer">http://en.wikipedia.org/wiki/Modular_arithmetic</a></p> <p>Basically, in a two's complement system, an n-bit number really represents an equivalence class of integers modulo 2^n.</p> <p>If that seems to make it more complicated instead of less, then the key things to know are simply:</p> <ul> <li>An unsigned n-bit number holds values from 0 to 2^n-1. The values "wrap around", so e.g., when you add two numbers and get 2^n, you really get zero. (This is called "overflow".)</li> <li>A signed n-bit number holds values from -2^(n-1) to 2^(n-1)-1. Numbers still wrap around, but the highest number wraps around to the most negative, and it starts counting up towards zero from there.</li> </ul> <p>So, an unsigned byte (8-bit number) can be 0 to 255. 255 + 1 wraps around to 0. 255 + 2 ends up as 1, and so forth. A signed byte can be -128 to 127. 127 + 1 ends up as -128. (!) 127 + 2 ends up as -127, etc.</p>

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