One's Complement: Integer ↗ Binary: 11 001 100 110 103 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 11 001 100 110 103(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;
  • 11 001 100 110 103 ÷ 2 = 5 500 550 055 051 + 1;
  • 5 500 550 055 051 ÷ 2 = 2 750 275 027 525 + 1;
  • 2 750 275 027 525 ÷ 2 = 1 375 137 513 762 + 1;
  • 1 375 137 513 762 ÷ 2 = 687 568 756 881 + 0;
  • 687 568 756 881 ÷ 2 = 343 784 378 440 + 1;
  • 343 784 378 440 ÷ 2 = 171 892 189 220 + 0;
  • 171 892 189 220 ÷ 2 = 85 946 094 610 + 0;
  • 85 946 094 610 ÷ 2 = 42 973 047 305 + 0;
  • 42 973 047 305 ÷ 2 = 21 486 523 652 + 1;
  • 21 486 523 652 ÷ 2 = 10 743 261 826 + 0;
  • 10 743 261 826 ÷ 2 = 5 371 630 913 + 0;
  • 5 371 630 913 ÷ 2 = 2 685 815 456 + 1;
  • 2 685 815 456 ÷ 2 = 1 342 907 728 + 0;
  • 1 342 907 728 ÷ 2 = 671 453 864 + 0;
  • 671 453 864 ÷ 2 = 335 726 932 + 0;
  • 335 726 932 ÷ 2 = 167 863 466 + 0;
  • 167 863 466 ÷ 2 = 83 931 733 + 0;
  • 83 931 733 ÷ 2 = 41 965 866 + 1;
  • 41 965 866 ÷ 2 = 20 982 933 + 0;
  • 20 982 933 ÷ 2 = 10 491 466 + 1;
  • 10 491 466 ÷ 2 = 5 245 733 + 0;
  • 5 245 733 ÷ 2 = 2 622 866 + 1;
  • 2 622 866 ÷ 2 = 1 311 433 + 0;
  • 1 311 433 ÷ 2 = 655 716 + 1;
  • 655 716 ÷ 2 = 327 858 + 0;
  • 327 858 ÷ 2 = 163 929 + 0;
  • 163 929 ÷ 2 = 81 964 + 1;
  • 81 964 ÷ 2 = 40 982 + 0;
  • 40 982 ÷ 2 = 20 491 + 0;
  • 20 491 ÷ 2 = 10 245 + 1;
  • 10 245 ÷ 2 = 5 122 + 1;
  • 5 122 ÷ 2 = 2 561 + 0;
  • 2 561 ÷ 2 = 1 280 + 1;
  • 1 280 ÷ 2 = 640 + 0;
  • 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.


11 001 100 110 103(10) = 1010 0000 0001 0110 0100 1010 1010 0000 1001 0001 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 11 001 100 110 103(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:

11 001 100 110 103(10) = 0000 0000 0000 0000 0000 1010 0000 0001 0110 0100 1010 1010 0000 1001 0001 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 11 001 100 110 102 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 11 001 100 110 104 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