One's Complement: Integer ↗ Binary: 110 111 011 087 Convert the Integer Number to a Signed Binary in One's Complement Representation. Write the Base Ten Decimal System Number as a Binary Code (Written in Base Two)

Signed integer number 110 111 011 087(10) converted and written as a signed binary in one's complement representation (base 2) = ?

1. 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;
  • 110 111 011 087 ÷ 2 = 55 055 505 543 + 1;
  • 55 055 505 543 ÷ 2 = 27 527 752 771 + 1;
  • 27 527 752 771 ÷ 2 = 13 763 876 385 + 1;
  • 13 763 876 385 ÷ 2 = 6 881 938 192 + 1;
  • 6 881 938 192 ÷ 2 = 3 440 969 096 + 0;
  • 3 440 969 096 ÷ 2 = 1 720 484 548 + 0;
  • 1 720 484 548 ÷ 2 = 860 242 274 + 0;
  • 860 242 274 ÷ 2 = 430 121 137 + 0;
  • 430 121 137 ÷ 2 = 215 060 568 + 1;
  • 215 060 568 ÷ 2 = 107 530 284 + 0;
  • 107 530 284 ÷ 2 = 53 765 142 + 0;
  • 53 765 142 ÷ 2 = 26 882 571 + 0;
  • 26 882 571 ÷ 2 = 13 441 285 + 1;
  • 13 441 285 ÷ 2 = 6 720 642 + 1;
  • 6 720 642 ÷ 2 = 3 360 321 + 0;
  • 3 360 321 ÷ 2 = 1 680 160 + 1;
  • 1 680 160 ÷ 2 = 840 080 + 0;
  • 840 080 ÷ 2 = 420 040 + 0;
  • 420 040 ÷ 2 = 210 020 + 0;
  • 210 020 ÷ 2 = 105 010 + 0;
  • 105 010 ÷ 2 = 52 505 + 0;
  • 52 505 ÷ 2 = 26 252 + 1;
  • 26 252 ÷ 2 = 13 126 + 0;
  • 13 126 ÷ 2 = 6 563 + 0;
  • 6 563 ÷ 2 = 3 281 + 1;
  • 3 281 ÷ 2 = 1 640 + 1;
  • 1 640 ÷ 2 = 820 + 0;
  • 820 ÷ 2 = 410 + 0;
  • 410 ÷ 2 = 205 + 0;
  • 205 ÷ 2 = 102 + 1;
  • 102 ÷ 2 = 51 + 0;
  • 51 ÷ 2 = 25 + 1;
  • 25 ÷ 2 = 12 + 1;
  • 12 ÷ 2 = 6 + 0;
  • 6 ÷ 2 = 3 + 0;
  • 3 ÷ 2 = 1 + 1;
  • 1 ÷ 2 = 0 + 1;

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

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


110 111 011 087(10) = 1 1001 1010 0011 0010 0000 1011 0001 0000 1111(2)


3. Determine the signed binary number bit length:

The base 2 number's actual length, in bits: 37.

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, 37,

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

=== is: 64.


4. Get the positive binary computer representation on 64 bits (8 Bytes):

If needed, add extra 0s in front (to the left) of the base 2 number, up to the required length, 64.


Number 110 111 011 087(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:

110 111 011 087(10) = 0000 0000 0000 0000 0000 0000 0001 1001 1010 0011 0010 0000 1011 0001 0000 1111

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 110 111 011 086 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 110 111 011 088 converted from decimal system (from base 10) and written as a signed binary in one's complement representation (written in base 2) = ?

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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