# Unsigned: Binary -> Integer: 1001 1000 1010 1011 0000 1011 1110 1101 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) 1001 1000 1010 1011 0000 1011 1110 1101_{(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^{31}

1 2^{30}

0 2^{29}

0 2^{28}

1 2^{27}

1 2^{26}

0 2^{25}

0 2^{24}

0 2^{23}

1 2^{22}

0 2^{21}

1 2^{20}

0 2^{19}

1 2^{18}

0 2^{17}

1 2^{16}

1 2^{15}

0 2^{14}

0 2^{13}

0 2^{12}

0 2^{11}

1 2^{10}

0 2^{9}

1 2^{8}

1 2^{7}

1 2^{6}

1 2^{5}

1 2^{4}

0 2^{3}

1 2^{2}

1 2^{1}

0 2^{0}

1

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

#### 1001 1000 1010 1011 0000 1011 1110 1101_{(2)} =

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

#### (2 147 483 648 + 0 + 0 + 268 435 456 + 134 217 728 + 0 + 0 + 0 + 8 388 608 + 0 + 2 097 152 + 0 + 524 288 + 0 + 131 072 + 65 536 + 0 + 0 + 0 + 0 + 2 048 + 0 + 512 + 256 + 128 + 64 + 32 + 0 + 8 + 4 + 0 + 1)_{(10)} =

#### (2 147 483 648 + 268 435 456 + 134 217 728 + 8 388 608 + 2 097 152 + 524 288 + 131 072 + 65 536 + 2 048 + 512 + 256 + 128 + 64 + 32 + 8 + 4 + 1)_{(10)} =

#### 2 561 346 541_{(10)}

## The number 1001 1000 1010 1011 0000 1011 1110 1101_{(2)} converted from an unsigned binary (in base 2) and written as a positive integer (with no sign) in decimal system (in base ten):

1001 1000 1010 1011 0000 1011 1110 1101_{(2)} = 2 561 346 541_{(10)}

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

## Convert unsigned binary numbers (base two) to positive integers in the decimal system (base ten)

### How to convert an unsigned binary number (base two) to a positive integer in base ten:

#### 1) Multiply each bit of the binary number by its corresponding power of 2 that its place value represents.

#### 2) Add all the terms up to get the integer number in base ten.