# Converter to signed binary in one's complement representation: converting decimal system (base 10) signed integer numbers

## Convert signed integer numbers from the decimal system (base ten) to signed binary one's complement representation

### How to convert a base 10 signed integer number to signed binary in one's complement representation:

#### 1) Divide the positive version of number repeatedly by 2, keeping track of each remainder, till getting a quotient that is 0.

#### 2) Construct the base 2 representation by taking the previously calculated remainders starting from the last remainder up to the first one, in that order.

#### 3) Construct the positive binary computer representation so that the first bit is 0.

#### 4) Only if the initial number is negative, switch all the bits from 0 to 1 and from 1 to 0 (reversing the digits).

## Latest signed integer numbers converted from decimal system to signed binary in one's complement representation

** Signed integer -300 converted from decimal system (base 10) to signed binary one's complement representation = ? ** | * May 29 15:20 UTC (GMT)* |

** Signed integer 75 converted from decimal system (base 10) to signed binary one's complement representation = ? ** | * May 29 15:20 UTC (GMT)* |

** Signed integer -9,333,836 converted from decimal system (base 10) to signed binary one's complement representation = ? ** | * May 29 15:19 UTC (GMT)* |

** Signed integer 10,011,011,001,118 converted from decimal system (base 10) to signed binary one's complement representation = ? ** | * May 29 15:14 UTC (GMT)* |

** Signed integer 314,149 converted from decimal system (base 10) to signed binary one's complement representation = ? ** | * May 29 15:01 UTC (GMT)* |

** Signed integer 2,022 converted from decimal system (base 10) to signed binary one's complement representation = ? ** | * May 29 15:01 UTC (GMT)* |

** Signed integer 1,234,537 converted from decimal system (base 10) to signed binary one's complement representation = ? ** | * May 29 15:01 UTC (GMT)* |

** Signed integer 48,342 converted from decimal system (base 10) to signed binary one's complement representation = ? ** | * May 29 14:59 UTC (GMT)* |

** Signed integer -12,205 converted from decimal system (base 10) to signed binary one's complement representation = ? ** | * May 29 14:58 UTC (GMT)* |

** Signed integer 10,000,014 converted from decimal system (base 10) to signed binary one's complement representation = ? ** | * May 29 14:57 UTC (GMT)* |

** Signed integer 9,420 converted from decimal system (base 10) to signed binary one's complement representation = ? ** | * May 29 14:56 UTC (GMT)* |

** Signed integer 7,755 converted from decimal system (base 10) to signed binary one's complement representation = ? ** | * May 29 14:56 UTC (GMT)* |

** Signed integer 600,520,203,909,999,977 converted from decimal system (base 10) to signed binary one's complement representation = ? ** | * May 29 14:51 UTC (GMT)* |

**All decimal integer numbers converted to signed binary one's complement representation ** |

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

### Follow the steps below to convert a signed base 10 integer number to signed binary in one's complement representation:

- 1. If the number to be converted is negative, start with the positive version of the number.
- 2. Divide repeatedly by 2 the positive representation of the integer number that is to be converted to binary, keeping track of each remainder, until we get a quotient that is equal to ZERO.
- 3. Construct the base 2 representation of the positive number, by taking all the remainders starting from the bottom of the list constructed above. Thus, the last remainder of the divisions becomes the first symbol (the leftmost) of the base two number, while the first remainder becomes the last symbol (the rightmost).
- 4. Binary numbers represented in computer language must have 4, 8, 16, 32, 64, ... bit length (a power of 2) - if needed, fill in '0' bits in front (to the left) of the base 2 number calculated above, up to the right length; this way the first bit (leftmost) will always be '0', correctly representing a positive number.
- 5. To get the negative integer number representation in signed binary one's complement, replace all '0' bits with '1's and all '1' bits with '0's.

### Example: convert the negative number -49 from the decimal system (base ten) to signed binary one's complement:

- 1. Start with the positive version of the number: |-49| = 49
- 2. Divide repeatedly 49 by 2, keeping track of each remainder:
- division = quotient +
**remainder**
- 49 ÷ 2 = 24 +
**1**
- 24 ÷ 2 = 12 +
**0**
- 12 ÷ 2 = 6 +
**0**
- 6 ÷ 2 = 3 +
**0**
- 3 ÷ 2 = 1 +
**1**
- 1 ÷ 2 = 0 +
**1**

- 3. Construct the base 2 representation of the positive number, by taking all the remainders starting from the bottom of the list constructed above:

49_{(10)} = 11 0001_{(2)} - 4. The actual bit length of base 2 representation is 6, so the positive binary computer representation of a signed binary will take in this case 8 bits (the least power of 2 that is larger than 6) - add '0's in front of the base 2 number, up to the required length:

49_{(10)} = 0011 0001_{(2)} - 5. To get the negative integer number representation in signed binary one's complement, replace all '0' bits with '1's and all '1' bits with '0's:

-49_{(10)} = 1100 1110 #### Number -49_{(10)}, signed integer, converted from the decimal system (base 10) to signed binary in one's complement representation = 1100 1110