Some Terms

Computer memory is a numbered sequence of fixed-size storage locations. The number attached to each storage location is called its address. The size of a single storage location is called a byte. On x86 processors, a byte is a number between 0 and 255.

You may be wondering how computers can display and use text, graphics, and even large numbers when all they can do is store numbers between 0 and 255. First of all, specialized hardware like graphics cards have special interpretations of each number. When displaying to the screen, the computer uses ASCII code tables to translate the numbers you are sending it into letters to display on the screen, with each number translating to exactly one letter or numeral.^[1] For example, the capital letter A is represented by the number 65. The numeral 1 is represented by the number 49. So, to print out "HELLO", you would actually give the computer the sequence of numbers 72, 69, 76, 76, 79. To print out the number 100, you would give the computer the sequence of numbers 49, 48, 48. A list of ASCII characters and their numeric codes is found in Appendix D.

In addition to using numbers to represent ASCII characters, you as the programmer get to make the numbers mean anything you want them to, as well. For example, if I am running a store, I would use a number to represent each item I was selling. Each number would be linked to a series of other numbers which would be the ASCII codes for what I wanted to display when the items were scanned in. I would have more numbers for the price, how many I have in inventory, and so on.

So what about if we need numbers larger than 255? We can simply use a combination of bytes to represent larger numbers. Two bytes can be used to represent any number between 0 and 65535. Four bytes can be used to represent any number between 0 and 4294967295. Now, it is quite difficult to write programs to stick bytes together to increase the size of your numbers, and requires a bit of math. Luckily, the computer will do it for us for numbers up to 4 bytes long. In fact, four-byte numbers are what we will work with by default.

We mentioned earlier that in addition to the regular memory that the computer has, it also has special-purpose storage locations called registers. Registers are what the computer uses for computation. Think of a register as a place on your desk - it holds things you are currently working on. You may have lots of information tucked away in folders and drawers, but the stuff you are working on right now is on the desk. Registers keep the contents of numbers that you are currently manipulating.

On the computers we are using, registers are each four bytes long. The size of a typical register is called a computer's word size. x86 processors have four-byte words. This means that it is most natural on these computers to do computations four bytes at a time.^[2] This gives us roughly 4 billion values.

Addresses are also four bytes (1 word) long, and therefore also fit into a register. x86 processors can access up to 4294967296 bytes if enough memory is installed. Notice that this means that we can store addresses the same way we store any other number. In fact, the computer can't tell the difference between a value that is an address, a value that is a number, a value that is an ASCII code, or a value that you have decided to use for another purpose. A number becomes an ASCII code when you attempt to display it. A number becomes an address when you try to look up the byte it points to. Take a moment to think about this, because it is crucial to understanding how computer programs work.

Addresses which are stored in memory are also called pointers, because instead of having a regular value in them, they point you to a different location in memory.

As we've mentioned, computer instructions are also stored in memory. In fact, they are stored exactly the same way that other data is stored. The only way the computer knows that a memory location is an instruction is that a special-purpose register called the instruction pointer points to them at one point or another. If the instruction pointer points to a memory word, it is loaded as an instruction. Other than that, the computer has no way of knowing the difference between programs and other types of data.^[3]

^[1]With the advent of international character sets and Unicode, this is not entirely true anymore. However, for the purposes of keeping this simple for beginners, we will use the assumption that one number translates directly to one character. For more information, see Appendix D.

^[2]Previous incarnations of x86 processors only had two-byte words. Therefore, most other literature dealing with x86 processors refers to two-byte entities as words for historical reasons, and therefore refer to four-byte entities as double-words. We are using the term word to mean the normal register size of a computer, which in this case is four bytes. More information is available in Appendix B,

^[3]Note that here we are talking about general computer theory. Some processors and operating systems actually mark the regions of memory that can be executed with a special marker that indicates this.