# Signed binary one's complement number 0000 0000 0000 0010 0010 0101 0001 0111 converted to decimal system (base ten) signed integer

## Signed binary one's complement 0000 0000 0000 0010 0010 0101 0001 0111_{(2)} to an integer in decimal system (in base 10) = ?

### 1. Is this a positive or a negative number?

#### In a signed binary one's complement,

#### The first bit (the leftmost) indicates the sign,

#### 1 = negative, 0 = positive.

#### 0000 0000 0000 0010 0010 0101 0001 0111 is the binary representation of a positive integer, on 32 bits (4 Bytes).

### 2. Get the binary representation of the positive (unsigned) number:

#### * Run this step only if the number is negative *

#### Flip all the bits in the signed binary one's complement representation (reverse the digits) - replace the bits set on 1 with 0s and the bits on 0 with 1s:

#### * Not the case - the number is positive *

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

2^{31}

0 2^{30}

0 2^{29}

0 2^{28}

0 2^{27}

0 2^{26}

0 2^{25}

0 2^{24}

0 2^{23}

0 2^{22}

0 2^{21}

0 2^{20}

0 2^{19}

0 2^{18}

0 2^{17}

1 2^{16}

0 2^{15}

0 2^{14}

0 2^{13}

1 2^{12}

0 2^{11}

0 2^{10}

1 2^{9}

0 2^{8}

1 2^{7}

0 2^{6}

0 2^{5}

0 2^{4}

1 2^{3}

0 2^{2}

1 2^{1}

1 2^{0}

1

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

#### 0000 0000 0000 0010 0010 0101 0001 0111_{(2)} =

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

#### (0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 131 072 + 0 + 0 + 0 + 8 192 + 0 + 0 + 1 024 + 0 + 256 + 0 + 0 + 0 + 16 + 0 + 4 + 2 + 1)_{(10)} =

#### (131 072 + 8 192 + 1 024 + 256 + 16 + 4 + 2 + 1)_{(10)} =

#### 140 567_{(10)}

### 5. If needed, adjust the sign of the integer number by the first digit (leftmost) of the signed binary:

#### 0000 0000 0000 0010 0010 0101 0001 0111_{(2)} = 140 567_{(10)}

## Number 0000 0000 0000 0010 0010 0101 0001 0111_{(2)} converted from signed binary one's complement representation to an integer in decimal system (in base 10):

0000 0000 0000 0010 0010 0101 0001 0111_{(2)} = 140 567_{(10)}

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

### More operations of this kind:

## Convert signed binary one's complement numbers to decimal system (base ten) integers

#### Entered binary number length must be: 2, 4, 8, 16, 32, or 64 - otherwise extra bits on 0 will be added in front (to the left).

### How to convert a signed binary number in one's complement representation to an integer in base ten:

#### 1) In a signed binary one's complement, first bit (leftmost) indicates the sign, 1 = negative, 0 = positive.

#### 2) Construct the unsigned binary number: flip all the bits in the signed binary one's complement representation (reversing the digits) - replace the bits set on 1 with 0s and the bits on 0 with 1s.

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

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

#### 5) Adjust the sign of the integer number by the first bit of the initial binary number.

## Latest binary numbers in one's complement representation converted to signed integers numbers in decimal system (base ten)

** 0000 0000 0000 0010 0010 0101 0001 0111 converted from: signed binary one's complement representation, to signed integer = 140,567 ** | * May 29 15:52 UTC (GMT)* |

** 1111 0000 0000 0000 0000 0000 0000 0010 converted from: signed binary one's complement representation, to signed integer = -268,435,453 ** | * May 29 15:51 UTC (GMT)* |

** 1010 1011 converted from: signed binary one's complement representation, to signed integer = -84 ** | * May 29 15:50 UTC (GMT)* |

** 1010 1101 0100 0011 converted from: signed binary one's complement representation, to signed integer = -21,180 ** | * May 29 15:49 UTC (GMT)* |

** 1010 1011 converted from: signed binary one's complement representation, to signed integer = -84 ** | * May 29 15:48 UTC (GMT)* |

** 1111 0101 1101 0101 converted from: signed binary one's complement representation, to signed integer = -2,602 ** | * May 29 15:48 UTC (GMT)* |

** 0010 0110 1000 1100 converted from: signed binary one's complement representation, to signed integer = 9,868 ** | * May 29 15:46 UTC (GMT)* |

** 1011 converted from: signed binary one's complement representation, to signed integer = -4 ** | * May 29 15:46 UTC (GMT)* |

** 0000 0000 1010 1110 1010 1110 0111 0010 0110 0010 1001 0010 1000 1110 0111 1110 converted from: signed binary one's complement representation, to signed integer = 49,168,452,250,930,814 ** | * May 29 15:43 UTC (GMT)* |

** 0000 0000 0000 0001 0101 1001 1011 1100 converted from: signed binary one's complement representation, to signed integer = 88,508 ** | * May 29 15:43 UTC (GMT)* |

** 0000 0000 0000 0000 0000 0111 1011 1011 converted from: signed binary one's complement representation, to signed integer = 1,979 ** | * May 29 15:42 UTC (GMT)* |

** 1000 0001 0011 0110 converted from: signed binary one's complement representation, to signed integer = -32,457 ** | * May 29 15:42 UTC (GMT)* |

** 1000 1010 0011 0000 converted from: signed binary one's complement representation, to signed integer = -30,159 ** | * May 29 15:41 UTC (GMT)* |

** All the converted signed binary one's complement numbers ** |

## How to convert signed binary numbers in one's complement representation from binary system to decimal

### To understand how to convert a signed binary number in one's complement representation from binary system to decimal (base ten), the easiest way is to do it through an example - convert binary, 1001 1101, to base ten: