Difference between binary and decimal numbers?

The binary system has only two digits: 0 and 1

The decimal has ten digits: 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9

In binary, numbers are expressed as linear combinations of powers of 2 as in

13 = 1*23 + 1*22 + 0*21 + 1*20 which is written as 1101

In decimal, they are expressed in terms of powers of 10:

1507 = 1*103 + 5*102 + 0*21 + 7*20

All rules of mathematical operations (addition, subtraction, multiplication, division, exponents, etc) apply to both systems in the same way.