# Unsigned: Binary -> Integer: 10 0000 0100 0001 0000 1000 0100 0011 0010 Convert Base Two (2) Number to Base Ten (10), The Unsigned Binary Converted to a Positive Integer, Written in the Decimal System

## The unsigned binary (in base two) 10 0000 0100 0001 0000 1000 0100 0011 0010_{(2)} to a positive integer (with no sign) in decimal system (in base ten) = ?

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

2^{33}

1 2^{32}

0 2^{31}

0 2^{30}

0 2^{29}

0 2^{28}

0 2^{27}

0 2^{26}

1 2^{25}

0 2^{24}

0 2^{23}

0 2^{22}

0 2^{21}

0 2^{20}

1 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}

1 2^{9}

0 2^{8}

0 2^{7}

0 2^{6}

0 2^{5}

1 2^{4}

1 2^{3}

0 2^{2}

0 2^{1}

1 2^{0}

0

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

#### 10 0000 0100 0001 0000 1000 0100 0011 0010_{(2)} =

#### (1 × 2^{33} + 0 × 2^{32} + 0 × 2^{31} + 0 × 2^{30} + 0 × 2^{29} + 0 × 2^{28} + 0 × 2^{27} + 1 × 2^{26} + 0 × 2^{25} + 0 × 2^{24} + 0 × 2^{23} + 0 × 2^{22} + 0 × 2^{21} + 1 × 2^{20} + 0 × 2^{19} + 0 × 2^{18} + 0 × 2^{17} + 0 × 2^{16} + 1 × 2^{15} + 0 × 2^{14} + 0 × 2^{13} + 0 × 2^{12} + 0 × 2^{11} + 1 × 2^{10} + 0 × 2^{9} + 0 × 2^{8} + 0 × 2^{7} + 0 × 2^{6} + 1 × 2^{5} + 1 × 2^{4} + 0 × 2^{3} + 0 × 2^{2} + 1 × 2^{1} + 0 × 2^{0})_{(10)} =

#### (8 589 934 592 + 0 + 0 + 0 + 0 + 0 + 0 + 67 108 864 + 0 + 0 + 0 + 0 + 0 + 1 048 576 + 0 + 0 + 0 + 0 + 32 768 + 0 + 0 + 0 + 0 + 1 024 + 0 + 0 + 0 + 0 + 32 + 16 + 0 + 0 + 2 + 0)_{(10)} =

#### (8 589 934 592 + 67 108 864 + 1 048 576 + 32 768 + 1 024 + 32 + 16 + 2)_{(10)} =

#### 8 658 125 874_{(10)}

## The number 10 0000 0100 0001 0000 1000 0100 0011 0010_{(2)} converted from an unsigned binary (in base 2) and written as a positive integer (with no sign) in decimal system (in base ten):

10 0000 0100 0001 0000 1000 0100 0011 0010_{(2)} = 8 658 125 874_{(10)}

#### Spaces were used to group digits: for binary, by 4, for decimal, by 3.