Lesson 1: Converting between hex, binary, and decimal.

    The first thing you must know to program in a low level language is the common number bases. Decides knowing the human base 10 decimal system, you also need to know hexadecamal an binary. At first I figured I could get by without this... Boy was I wrong. So, Lets start with hex.
    Hex is base 16. The range for a hex digit is 0-9 and then A-F. Hex is usually expressed in two characters at a time. Here are some examples of hex numbers: $3C, $AF, $0F, B4h. A leading dollar sign ($) or a trailing lowercase 'h' signifies that the number is a hex digit.
So how do you go from hex to our number system? Ill show you. Lets convert $3C. First you take the first digit (3) and multiply it by 16. 3*16=48. Then you take the second number (C), which is 12, and add it to the number before, 48. That gives us an anwser of 60. Therefore $3C = 60. Just for refrence, here are the hex letters and their decimal equivilants:

Now lets move on to binary. Binary is base 2, meaning the range of values is 0-1, which is called a bit. 8 bits make up a byte, which is the standard unit when dealing in binary. Converting to decimal from binary sounds harder than it actually is, so bare with me.
Binary is written with a percent sign (%) leading or a lowercase 'b' trailing. Lets take the following number, %10010101 and convert it to decimal. Each bit has a specific value: Using a grid, Conversion is really easy.

Range Of Values

Lets look at the range of values. For a byte, the highest is %11111111. Lets throw it in the table.

So, the range of values for a single byte is 0-255, leaving 256 different values(2^8=256).

Now lets look at a hex digit.

Well, the highest hex digit is $FF. Lets do the math.

F=15, so 15*16=240. 240+15=255

Hmmm. The range of values of a byte and a hex digit is the same. So, %11111111=$FF.

So, hex and binary are closly intertwined. This makes it easy to sonvert between them.

Converting between hex and binary

Technically, each hex chracter is called a nibble which is 4 bits, or half a byte. You will notice the range of values for a nibble is 0-F in hex, 0000-1111 in binary, and 0-15 in decimal.

So lets take %1011010 and convert it to hex.

First, take the back 4 bits: %1010. This converts to decimal as 10. 10 in hex is A.

Now lets take the rest: %101. You can imagine in a zero in front if you please, so lets convert %0101. That equals 5, in hex and decimal. So, take the two digits, and you come up with $5A.

Lets just check that. 5*16=80, 80+10=90.

So, in conclusion, each hex digit, 0-F, is a nibble, and two nibbles make up a byte.

Here is a quick lookup chart for nibbles:

You now know the basics of hex and binary, and how to convert between bases. If you don't get it now, don't worry. It will come eventually.