Binary Numbers

In everyday life we use a decimal system of numbers based on 10 digits of 0 to 9. There is no law of nature that says this must be 10; it is just something that we have inherited along with a calendar of 12 months and an alphabet of 26 letters. 

In fact numbers could be based on any division we want.  For example 12 would be a very useful as it is so easily divisible by thirds and quarters, which is why the dozen is still in common use.  However, numbers based on 12 would require 2 extra digits, resulting in something like 0,1,2,3,4,5,6,7,8,9,§,Ø for example. 

This is just academic though as the current numbering system is decimal, and it is here to stay.  But not everything can be based on 10.  Computers are only able to understand binary numbers based on 2 digits.The electrical current is either on or off in a circuit board; 1 for on and 0 for off. Computers communicate by pulses of electricity in everything they do and so all information is passed and stored in ones and zeros. As a result the binary system is the basis on which all digital images are created. Knowing how this works is not vital, but it does help to explain some of the terminology.

Even at the risk of stating the obvious it helps to explain how addition works. Adding a 1 increases the number until 9 is reached after which the 1 column returns to 0 and a 1 is added to the 10 column on the left. In other words 10 is made of 2 digits; one 10 and no ones.  So a number such as 256 consists of 2 hundreds, 5 tens and 6 ones.  As a result decimal columns increase in multiples of 10.

Binary works in just the same way.  But as there are only 2 digits, consisting of 0 and 1, the maximum value in each column can only be 1, and therefore the binary columns increase in multiples of 2 instead. Adding 1 plus 1 returns the 1 column to 0 and a 1 is added to the 2 column on the left.  
For Example:
• 2=”10”       (1x2 + 0x1)
• 10=”1010” (1x8 + 0x4 + 1x2 + 0x1)
The end result is that 255=11111111 (128+64+32...) which is 8 digits.  As each digit of 1 or 0 requires 1 Bit of computer information, it therefore needs 8 Bits to store the 256 tones in a digital image. This is where the term 8 Bit for scans and images comes from. 


A Puzzle:  Decimal numbers are based on 10 digits, whereas Binary numbers are based on only 10 digits instead.  The apparent contradiction makes sense if Binary numbers are understood.