Binary to Decimal - Concept

                                                 We all have seen binary codes. Collection of  0's and 1's in a long string are called as Binary codes. For example: 0001101110010101000011101. But these 0's and 1's also represents Decimal numbers. Computers use binary codes and not decimals, first we will see how binary and decimal are related together.

BINARY SYSTEMS:

Lets us consider some empty slots.      _ _ _ _ _

Binary codes should be read from Right to Left. It cant be changed.

First slot from Right represents value of 1, Second is value of 2, Third is value of 4, Fourth is value of 8, and the cycle continues by multiples of 2.

CONDITION:
1 means 'YES', 0 means 'NO'

For example: Putting 1 in the first slot (from right-left) and 0's in the remaining represents the value 1 (one).
                     00001 = 1
                     Putting 1 in second slot and 0's in remaining represents the value 2.
                     00010 = 2

If we want to represent the number 8 in decimal, for binary...
Remember the condition.

NO  YES  NO  NO  NO
(0)    (1)    (0)    (0)    (0)


01000 = 1000 = 8

If you got 1's in two or three places, just add the values of 1's.
0101 = value of 1 in first slot is 1, and value of third slot is 4. add it up gives the value.
0101 = 5

 NOTE: For mastering in Binary ,... just practice yourselves.