Binary Numbers
Number Representations and Conversions in Binary
Today's advanced technology is built on circuits and electric pulses of 1's and 0's.  The electronic circuits used in this technology, are called two-state or bistable.  This means that only two states are possible, either ON or OFF.  The ON state is usually represented by a 1 and the OFF state is represented by a 0.
ON  - 1
OFF  -  0

All programs and data are ultimately recognised as just patterns of 0's and 1's by the digital computer.  This system is called the binary system.  To understand this system, it is useful to think more carefully about a system with which most people are familiar, that is the decimal system.

In the decimal system, the symbols 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 are used to represent different values.  For example, let us write four thousand, seven hundred and sixty-three.

1000s   100s     10s      1s 
103      102      101      100
4       7       6       3
which would represent
(4 x 1000) + (7 x 100) + (6 x 10) + (3 x 1)  =  4763

In the binary system, just two symbols are used: 0 and 1.  Therefore any number must be represented by 0s and 1s only.  The picture below gives an idea of how binary numbers are represented.  Try to note the pattern of the numbers and their corresponding lights.

Instead of using thousands, hundreds, tens, and units as in the decimal system, we use (from left to right) 16s or 24, 8s or 23, 4s or 22, 2s or 21, and 1s or 20.

This means that in the binary system, the number

16s      8s      4s      2s      1s
 24       23      22       21      20
 1      1      0      1      0
would represent one lot of 16, one lot of 8, no lots of 4, one lot of 2 and finally no units, or else
(1 x 16) + (1 x 8) + (0 x 4) + (1 x 2) + (0 x 1)  =  26

A popular method for converting a decimal number into a binary number is by dividing the number by two, repeatedly.  For example, we have shown that 26 is written as 11010 in binary.  Let's check it out, using the repeated "division by 2" method.

Yes, 11010 does represent 26 in decimal.

Original web page by Andrew Calleja