# 0110 0101 1110 1010 0000 1100 0100 1101 Signed Binary Number in One's Complement Representation, Converted and Written as a Decimal System Integer Number (in Base Ten). Steps Explained in Detail

## Signed binary in one's complement representation 0110 0101 1110 1010 0000 1100 0100 1101_{(2)} converted to an integer in decimal system (in base ten) = ?

### The steps we'll go through to make the conversion:

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

#### Map the unsigned binary number's digits.

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

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

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

#### 0110 0101 1110 1010 0000 1100 0100 1101 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 of the signed binary in 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}

1 2^{29}

1 2^{28}

0 2^{27}

0 2^{26}

1 2^{25}

0 2^{24}

1 2^{23}

1 2^{22}

1 2^{21}

1 2^{20}

0 2^{19}

1 2^{18}

0 2^{17}

1 2^{16}

0 2^{15}

0 2^{14}

0 2^{13}

0 2^{12}

0 2^{11}

1 2^{10}

1 2^{9}

0 2^{8}

0 2^{7}

0 2^{6}

1 2^{5}

0 2^{4}

0 2^{3}

1 2^{2}

1 2^{1}

0 2^{0}

1

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

#### 0110 0101 1110 1010 0000 1100 0100 1101_{(2)} =

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

#### (0 + 1 073 741 824 + 536 870 912 + 0 + 0 + 67 108 864 + 0 + 16 777 216 + 8 388 608 + 4 194 304 + 2 097 152 + 0 + 524 288 + 0 + 131 072 + 0 + 0 + 0 + 0 + 0 + 2 048 + 1 024 + 0 + 0 + 0 + 64 + 0 + 0 + 8 + 4 + 0 + 1)_{(10)} =

#### (1 073 741 824 + 536 870 912 + 67 108 864 + 16 777 216 + 8 388 608 + 4 194 304 + 2 097 152 + 524 288 + 131 072 + 2 048 + 1 024 + 64 + 8 + 4 + 1)_{(10)} =

#### 1 709 837 389_{(10)}

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

#### 0110 0101 1110 1010 0000 1100 0100 1101_{(2)} = 1 709 837 389_{(10)}

## The signed binary number in one's complement representation 0110 0101 1110 1010 0000 1100 0100 1101_{(2)} converted and written as an integer in decimal system (base ten):

0110 0101 1110 1010 0000 1100 0100 1101_{(2)} = 1 709 837 389_{(10)}

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

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

#### Binary number's length must be: 2, 4, 8, 16, 32, 64 - or else extra bits on 0 are 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.

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

** Convert signed binary number written in one's complement representation 0110 0101 1110 1010 0000 1100 0100 1101, write it as a decimal system (base ten) integer ** | * Oct 03 14:09 UTC (GMT)* |

** Convert signed binary number written in one's complement representation 1100 1001 0000 0000 0000 0000 0001 0100, write it as a decimal system (base ten) integer ** | * Oct 03 14:09 UTC (GMT)* |

** Convert signed binary number written in one's complement representation 0101 0001 0010 0111 0000 0101 0000 0001, write it as a decimal system (base ten) integer ** | * Oct 03 14:08 UTC (GMT)* |

** Convert signed binary number written in one's complement representation 0000 0000 0001 1111 0000 0000 0000 0101, write it as a decimal system (base ten) integer ** | * Oct 03 14:08 UTC (GMT)* |

** Convert signed binary number written in one's complement representation 0000 0000 0000 0000 0000 0110 1010 1011 0010 1010 1010 1010 1101 0101 1111 1011, write it as a decimal system (base ten) integer ** | * Oct 03 14:08 UTC (GMT)* |

** Convert signed binary number written in one's complement representation 1111 1110 1111 1110 1111 1111 1111 1100, write it as a decimal system (base ten) integer ** | * Oct 03 14:08 UTC (GMT)* |

** Convert signed binary number written in one's complement representation 1000 0010 1010 1100, write it as a decimal system (base ten) integer ** | * Oct 03 14:08 UTC (GMT)* |

** Convert signed binary number written in one's complement representation 0000 0000 0100 0011, write it as a decimal system (base ten) integer ** | * Oct 03 14:08 UTC (GMT)* |

** Convert signed binary number written in one's complement representation 0101 1111 0011 1110, write it as a decimal system (base ten) integer ** | * Oct 03 14:07 UTC (GMT)* |

** Convert signed binary number written in one's complement representation 1100 1001, write it as a decimal system (base ten) integer ** | * Oct 03 14:07 UTC (GMT)* |

** Convert signed binary number written in one's complement representation 0110 1111, write it as a decimal system (base ten) integer ** | * Oct 03 14:07 UTC (GMT)* |

** Convert signed binary number written in one's complement representation 1101 1010 1110 1100, write it as a decimal system (base ten) integer ** | * Oct 03 14:07 UTC (GMT)* |

** Convert signed binary number written in one's complement representation 0000 1010 1010 0101, write it as a decimal system (base ten) integer ** | * Oct 03 14:07 UTC (GMT)* |

** All the signed binary numbers in one's complement representation converted to decimal system (base ten) integers ** |

## 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:

## Available Base Conversions Between Decimal and Binary Systems

### Conversions Between Decimal System Numbers (Written in Base Ten) and Binary System Numbers (Base Two and Computer Representation):

### 1. Integer -> Binary

### 2. Decimal -> Binary

### 3. Binary -> Integer

### 4. Binary -> Decimal