Unsigned binary number (base two) 1000 0000 1000 0000 1000 0000 1000 0001 converted to decimal system (base ten) positive integer

How to convert an unsigned binary (base 2): 1000 0000 1000 0000 1000 0000 1000 0001_{(2)} to a positive integer (no sign) in decimal system (in base 10)

1. Map the unsigned binary number's digits versus the corresponding powers of 2 that their place value represent:

2^{31}

1

2^{30}

0

2^{29}

0

2^{28}

0

2^{27}

0

2^{26}

0

2^{25}

0

2^{24}

0

2^{23}

1

2^{22}

0

2^{21}

0

2^{20}

0

2^{19}

0

2^{18}

0

2^{17}

0

2^{16}

0

2^{15}

1

2^{14}

0

2^{13}

0

2^{12}

0

2^{11}

0

2^{10}

0

2^{9}

0

2^{8}

0

2^{7}

1

2^{6}

0

2^{5}

0

2^{4}

0

2^{3}

0

2^{2}

0

2^{1}

0

2^{0}

1

2. Multiply each bit by its corresponding power of 2 and add all the terms up:

Number 1000 0000 1000 0000 1000 0000 1000 0001_{(2)} converted from unsigned binary (base 2) to positive integer (no sign) in decimal system (in base 10):

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: