How do we convert binary to decimal and decimal to binary?

Binary is the simplest kind of number system that uses only two digits of 0 and 1 (i.e. value of base 2). Since digital electronics have only these two states (either 0 or 1), so binary number is most preferred in modern computer engineer, networking and communication specialists, and other professionals.

Whereas Decimal number is most familiar number system to the general public. It is base 10 which has only 10 symbols: 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9.

Since number numbers are type of positional number system. That means weight of the positions from right to left are as 20, 21, 22, 23... and so on for the integer part and weight of the positions from left to right are as 2-1, 2-2, 2-3, 2-4... and so on for the fractional part.

Example:

Convert binary number 11001010 into decimal number. 

= (11001010)₂

= 1 x 2⁷ + 1 x 2⁶ + 0 x 2⁵ + 0 x 2⁴ + 1 x 2³ + 0 x 2² + 1 x 2¹ + 0 x 2⁰

= 128 + 64 + 0 + 0 + 8 + 0 + 2 + 0

= (202)₁₀