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)}

Binary unsigned number (base 2), 101 0011_{(2)} = 83_{(10)}, unsigned positive integer in base 10