One's Complement: Integer Number -1 112 426 191 Converted and Written as a Signed Binary in One's Complement Representation

Integer number -1 112 426 191(10) written as a signed binary in one's complement representation

1. Start with the positive version of the number:

|-1 112 426 191| = 1 112 426 191

2. Divide the number repeatedly by 2:

Keep track of each remainder.

We stop when we get a quotient that is equal to zero.


  • division = quotient + remainder;
  • 1 112 426 191 ÷ 2 = 556 213 095 + 1;
  • 556 213 095 ÷ 2 = 278 106 547 + 1;
  • 278 106 547 ÷ 2 = 139 053 273 + 1;
  • 139 053 273 ÷ 2 = 69 526 636 + 1;
  • 69 526 636 ÷ 2 = 34 763 318 + 0;
  • 34 763 318 ÷ 2 = 17 381 659 + 0;
  • 17 381 659 ÷ 2 = 8 690 829 + 1;
  • 8 690 829 ÷ 2 = 4 345 414 + 1;
  • 4 345 414 ÷ 2 = 2 172 707 + 0;
  • 2 172 707 ÷ 2 = 1 086 353 + 1;
  • 1 086 353 ÷ 2 = 543 176 + 1;
  • 543 176 ÷ 2 = 271 588 + 0;
  • 271 588 ÷ 2 = 135 794 + 0;
  • 135 794 ÷ 2 = 67 897 + 0;
  • 67 897 ÷ 2 = 33 948 + 1;
  • 33 948 ÷ 2 = 16 974 + 0;
  • 16 974 ÷ 2 = 8 487 + 0;
  • 8 487 ÷ 2 = 4 243 + 1;
  • 4 243 ÷ 2 = 2 121 + 1;
  • 2 121 ÷ 2 = 1 060 + 1;
  • 1 060 ÷ 2 = 530 + 0;
  • 530 ÷ 2 = 265 + 0;
  • 265 ÷ 2 = 132 + 1;
  • 132 ÷ 2 = 66 + 0;
  • 66 ÷ 2 = 33 + 0;
  • 33 ÷ 2 = 16 + 1;
  • 16 ÷ 2 = 8 + 0;
  • 8 ÷ 2 = 4 + 0;
  • 4 ÷ 2 = 2 + 0;
  • 2 ÷ 2 = 1 + 0;
  • 1 ÷ 2 = 0 + 1;

3. Construct the base 2 representation of the positive number:

Take all the remainders starting from the bottom of the list constructed above.


1 112 426 191(10) = 100 0010 0100 1110 0100 0110 1100 1111(2)


4. Determine the signed binary number bit length:

The base 2 number's actual length, in bits: 31.

A signed binary's bit length must be equal to a power of 2, as of:

21 = 2; 22 = 4; 23 = 8; 24 = 16; 25 = 32; 26 = 64; ...

The first bit (the leftmost) indicates the sign:

0 = positive integer number, 1 = negative integer number


The least number that is:

1) a power of 2

2) and is larger than the actual length, 31,

3) so that the first bit (leftmost) could be zero
(we deal with a positive number at this moment)

=== is: 32.


5. Get the positive binary computer representation on 32 bits (4 Bytes):

If needed, add extra 0s in front (to the left) of the base 2 number, up to the required length, 32.


1 112 426 191(10) = 0100 0010 0100 1110 0100 0110 1100 1111


6. Get the negative integer number representation:

To write the negative integer number on 32 bits (4 Bytes),

as a signed binary in one's complement representation,

... replace all the bits on 0 with 1s and all the bits set on 1 with 0s.


Reverse the digits, flip the digits:

Replace the bits set on 0 with 1s and the bits set on 1 with 0s.

-1 112 426 191(10) = !(0100 0010 0100 1110 0100 0110 1100 1111)


Number -1 112 426 191(10), a signed integer number (with sign), converted from decimal system (from base 10) and written as a signed binary in one's complement representation:

-1 112 426 191(10) = 1011 1101 1011 0001 1011 1001 0011 0000

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

More operations on signed integers written as signed binary numbers in one's complement representation:

» Signed integer number -1 112 426 192 converted from decimal system (from base 10) and written as a signed binary in one's complement representation (written in base 2) = ?

» Signed integer number -1 112 426 190 converted from decimal system (from base 10) and written as a signed binary in one's complement representation (written in base 2) = ?

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