Friday, 26 August 2011

Counting with Binary Quick Tip

People have ten fingers and so our system of counting seems
to have developed around human anatomy, the hands. A computers' anatomy revolves around a yes or no system. It has two fingers so to speak and those are represented by zeros and ones.

Every digit in the 10 base system is a multiple of 10 starting with the left most digit being 10 and the next one 10 x 10, the one after that is 10x 10 x10 and so on.
For example lets examine the number below

123456

6 x 1 = 6
5 x 10 = 50
4 x 100 = 400
3 x 1000 = 3 000
2 x 10000 = 20 000
1 x 100000 = 100 000

The above is a break down of the number 123456. Adding all the numbers together supplies the answer.

Now  lets examine a binary number and see what its decimal equivalent is.

1001001

1 x 1 = 1
0 x 2 = 0
0 x 4 = 0
1 x 8 = 8
0 x 16 = 0
0 x 32 = 0
1 x 64 = 64

All these add up to 73. Which is the equivalent to the binary number 1001001

Every digit from the left is mulitlied by 2 exactly like the decimal system is multiplied by 10.

Computer Science Illuminated, Fourth Edition

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