## 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 the 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 power of 2 (numeral base) that its place value represents, starting with zero, from the right of the number (rightmost bit), walking to the left of the number, increasing each corresponding power of 2 by exactly one unit each time we move to the left:
powers of 2: 6 5 4 3 2 1 0 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 adding all the terms up:
#### 101 0011

_{(2)}=#### (1 × 2

^{6}+ 0 × 2^{5}+ 1 × 2^{4}+ 0 × 2^{3}+ 0 × 2^{2}+ 1 × 2^{1}+ 1 × 2^{0})_{(10)}=#### (64 + 0 + 16 + 0 + 0 + 2 + 1)

_{(10)}=#### (64 + 16 + 2 + 1)

_{(10)}=#### 83

_{(10)} #### Binary unsigned number (base 2), 101 0011

_{(2)}= 83_{(10)}, unsigned positive integer in base 10