## How to convert unsigned binary numbers from binary system to decimal = simply convert from base two to base ten

### To understand how to convert a number from base two to base ten, the easiest way is to do it through an example - convert number from base two, 101 0011_{(2)}, to base ten:

- Write bellow the binary number in base two, and above each bit that makes up the binary number write the corresponding powers of 2 (numeral base), starting with zero, from the right of the number (rightmost bit), walking to the left of the number, increasing each corresonding power of 2 with exactly one unit:
powers of 2 6 5 4 3 2 1 0 number's digits 1 0 1 0 0 1 1 - Build the representation of the positive number in base 10, by taking each digit of the binary number, multiplying it by the corresponding power of 2 and then summing up all the terms:

101 0011_{(2)}=

1 * 2^{6}+ 0 * 2^{5}+ 1 * 2^{4}+ 0 * 2^{3}+ 0 * 2^{2}+ 1 * 2^{1}+ 1 * 2^{0}=

= 64 + 0 + 16 + 0 + 0 + 2 + 1 =

= 64 + 16 + 2 + 1 =

= 83_{(10)}