Numbering Systems

The binary and hexidecimal numbering systems have always presented a huge problem for most students. Actually, if I look through the different computer books and study material that try to explain the subject, its really no wonder. I have found information that explains it using boxes, building blocks, candles, cars.... I have no idea what this is myself. In fact, just as you start to think you've got a handle on it, you read another explanation that tends to confuse you entirely. So, at the risk of baffling you completely, I'll try to explain, using another method, the method my grade 2 teacher (or maybe grade 3, I can't remember) taught me to understand decimal numbers of more than 1 digit. This doesn't work so well for hexidecimal, because the numbers get real large real quick. But we can check it out.

First thing to remember... is that you don't need to learn to count. Unless you're attempting to understand low level programming, learning binary provides you with two things:
- comprehension of how your computer stores information, with a better understanding of bits, bytes, kilobytes, etc...
- an easy method of converting between decimal and hexidecimal. You don't have to learn to count in hexidecimal either, but I/O addresses and memory addresses are given in hex and sometimes you can resolve device conflicts by being able to tell if addresses overlap.

So, my suggestion is to find a conversion method that you can understand, bookmark it or keep it in a file, then forget about it. Look it up again on the rare occasion that you might need it. (By the way, my favorite conversion method is a calculator).

All that being said, lets get back to grade 2.

Decimal (base 10)
The decimal numbering system is the system we all use in our everyday work. It consists of 10 digits (hence the name decimal). The digits, from smallest to largest are:
0, 1, 2, 3, 4, 5, 6, 7, 8, 9.

Now, any number can be broken down into columns. From right to left, the first column is the 1's column, then the 10's column, then the 100's, then the 1000's, etc..
Let's look at the number 137:

0 X 1000 = 0 (0 thousands)
1 X 100 = 100 (1 hundreds)
3 X 10 = 30 (3 tens)
7 X 1 = 7 (7 ones)

0+100 + 30 + 7 = 137

If you don't understand it this far, go back over it until you do, or get some help.

OK, lets try the number 77:

0 X 1000 = 0 (0 thousands)
0 X 100 = 0 (0 hundreds)
7 X 10 = 70 (7 tens)
7 X 1 = 7 (7 ones)

0+0+70 + 7 = 77

If you understand this far, go on to the next page for binary.

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