One's Complement: Integer ↗ Binary: 11 011 001 011 031 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 11 011 001 011 031(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;
  • 11 011 001 011 031 ÷ 2 = 5 505 500 505 515 + 1;
  • 5 505 500 505 515 ÷ 2 = 2 752 750 252 757 + 1;
  • 2 752 750 252 757 ÷ 2 = 1 376 375 126 378 + 1;
  • 1 376 375 126 378 ÷ 2 = 688 187 563 189 + 0;
  • 688 187 563 189 ÷ 2 = 344 093 781 594 + 1;
  • 344 093 781 594 ÷ 2 = 172 046 890 797 + 0;
  • 172 046 890 797 ÷ 2 = 86 023 445 398 + 1;
  • 86 023 445 398 ÷ 2 = 43 011 722 699 + 0;
  • 43 011 722 699 ÷ 2 = 21 505 861 349 + 1;
  • 21 505 861 349 ÷ 2 = 10 752 930 674 + 1;
  • 10 752 930 674 ÷ 2 = 5 376 465 337 + 0;
  • 5 376 465 337 ÷ 2 = 2 688 232 668 + 1;
  • 2 688 232 668 ÷ 2 = 1 344 116 334 + 0;
  • 1 344 116 334 ÷ 2 = 672 058 167 + 0;
  • 672 058 167 ÷ 2 = 336 029 083 + 1;
  • 336 029 083 ÷ 2 = 168 014 541 + 1;
  • 168 014 541 ÷ 2 = 84 007 270 + 1;
  • 84 007 270 ÷ 2 = 42 003 635 + 0;
  • 42 003 635 ÷ 2 = 21 001 817 + 1;
  • 21 001 817 ÷ 2 = 10 500 908 + 1;
  • 10 500 908 ÷ 2 = 5 250 454 + 0;
  • 5 250 454 ÷ 2 = 2 625 227 + 0;
  • 2 625 227 ÷ 2 = 1 312 613 + 1;
  • 1 312 613 ÷ 2 = 656 306 + 1;
  • 656 306 ÷ 2 = 328 153 + 0;
  • 328 153 ÷ 2 = 164 076 + 1;
  • 164 076 ÷ 2 = 82 038 + 0;
  • 82 038 ÷ 2 = 41 019 + 0;
  • 41 019 ÷ 2 = 20 509 + 1;
  • 20 509 ÷ 2 = 10 254 + 1;
  • 10 254 ÷ 2 = 5 127 + 0;
  • 5 127 ÷ 2 = 2 563 + 1;
  • 2 563 ÷ 2 = 1 281 + 1;
  • 1 281 ÷ 2 = 640 + 1;
  • 640 ÷ 2 = 320 + 0;
  • 320 ÷ 2 = 160 + 0;
  • 160 ÷ 2 = 80 + 0;
  • 80 ÷ 2 = 40 + 0;
  • 40 ÷ 2 = 20 + 0;
  • 20 ÷ 2 = 10 + 0;
  • 10 ÷ 2 = 5 + 0;
  • 5 ÷ 2 = 2 + 1;
  • 2 ÷ 2 = 1 + 0;
  • 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.


11 011 001 011 031(10) = 1010 0000 0011 1011 0010 1100 1101 1100 1011 0101 0111(2)


3. Determine the signed binary number bit length:

The base 2 number's actual length, in bits: 44.

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, 44,

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 11 011 001 011 031(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:

11 011 001 011 031(10) = 0000 0000 0000 0000 0000 1010 0000 0011 1011 0010 1100 1101 1100 1011 0101 0111

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 11 011 001 011 030 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 11 011 001 011 032 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