What Is The Binary Number System And How Is It Different Form The Decimal Number System?

The binary system uses 1 and 0 whereas the decimal system uses 0 to 9.  The difference is the number of digits it uses.

Binary code consists of just 1+0,the mayans were aware of all matter consisting of these numbers in different sequences,phytagarus believed all matter consists of 1-9

Binary uses only the number 0 and 1. You count in the order; 1, 10,11, 100,101, 111, 1000,1001,1010,1011,1100,1101,1110,1111......These equate to 1,2,3,4,5,6,7,8,8,10 11,12 13 and 14.
To add 2 binary numbers the sum is the same as decimal but instead of putting a zero when the numbers add up to 10 and carrying 1 forward you put a zero when they add up to 2 and then carry one forward. Therefore 110
                                +101  
                              =1010
Hope that helps