A Bit About Binary

Humans use the decimal (base-ten) numbering system, which is made up of the digits "0" to "9".
Computers only understand "off" and "on". This is easily represented with the binary (base-two) numbering system, which uses the digits "0" and "1".
So, do you have to be some kind of mathematical genius, or a computer yourself, to understand the binary numbering system? Not at all!
Using only 16 scraps of paper, a pen or pencil, and grade-school-level math you (yes, you) can master the binary numbering system in a matter of minutes! How, you ask? Read on!

Setting Up:
Tear eight strips of paper, lay them horizontally side by side, and label them from right to left "0" to "7". So you'll have:

Now put a scrap of paper above each strip. Write a "1" on the scrap above strip 0. For strips "1" - "7" the number on the scrap above will be double whatever was on the previous scrap. So strip 1 will be "2", strip 2 will be "4", etc. You should end up with:

Example 1:
Okay, that's it for the set up; now for the fun part!
Turn strip 1 and strip 3 so that they're vertical:

				8		2		8 + 2 = 10
0	0	0	0	1	0	1	0	00001010

Strip 3 is pointing to the "8", and strip 1 points to "2". 8 + 2 = 10, so this is how the number "10" would look in binary. If you write down a "0" for each horizontal strip & a "1" for each vertical strip you get "0 0 0 0 1 0 1 0".

Example 2:
Let's try another. Set strips 0, 2, 3, and 5 vertical, and the others horizontal:

		32		8	4		1	32 + 8 + 4 + 1 = 45
0	0	1	0	1	1	0	1	00101101

So we have the numbers "32" (strip 5), "8" (strip 3), "4" (strip 2), and "1" (strip 0). Added together, that's... um... 45 ("00101101" in binary).

Some Tech Terms (Hey; keep reading!):

• Each strip of paper is a "bit" (binary digit), and it can either be a "0" (or horizontal, off, or false) or a "1" (or vertical, on, or true).
• Four bits compose a "nybble". A nybble's value ranges from "0" (0000) to "15" (1111); 16 possibilities.
• Eight bits make up one "byte". A byte has 256 possible values, from "0" (00000000) to 255 (11111111).
• Bits are numbered from right to left. The bit farthest to the right is always bit 0. ...No foolin'.
• A bit's value is 2 raised the the power of the bit's number (or, more simply, double the value of the preceeding bit).
  So bit 8 would equal 256 (2^8), bit 9 would be 512 (2^9), and so on.
• 16-bits can represent any number between 0 and 65,535.
• At 24 bits, you have over 16 million possibilities.
• 32-bit numbers range from 0 to over 4 billion.

Test Your Knowledge:
Keeping in mind that "0" is a horizontal strip and "1" is a vertical one, what are the decimal values for:

1.   0 0 0 0 0 0 1 1
2.   1 0 0 0 0 0 1 0
3.   1 1 1 1 1 1 1 0
4.   1 0 1
   ...Ha, a trick! Just remember that the rightmost bit is always bit (or strip) number 0.
5.   0 0 0 0 1 1 1 1

Remember, there are only 10 kinds of people in the world: those who understand binary, and those who don't!