One's Complement: Integer ↗ Binary: 1 000 101 009 959 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 1 000 101 009 959(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;
  • 1 000 101 009 959 ÷ 2 = 500 050 504 979 + 1;
  • 500 050 504 979 ÷ 2 = 250 025 252 489 + 1;
  • 250 025 252 489 ÷ 2 = 125 012 626 244 + 1;
  • 125 012 626 244 ÷ 2 = 62 506 313 122 + 0;
  • 62 506 313 122 ÷ 2 = 31 253 156 561 + 0;
  • 31 253 156 561 ÷ 2 = 15 626 578 280 + 1;
  • 15 626 578 280 ÷ 2 = 7 813 289 140 + 0;
  • 7 813 289 140 ÷ 2 = 3 906 644 570 + 0;
  • 3 906 644 570 ÷ 2 = 1 953 322 285 + 0;
  • 1 953 322 285 ÷ 2 = 976 661 142 + 1;
  • 976 661 142 ÷ 2 = 488 330 571 + 0;
  • 488 330 571 ÷ 2 = 244 165 285 + 1;
  • 244 165 285 ÷ 2 = 122 082 642 + 1;
  • 122 082 642 ÷ 2 = 61 041 321 + 0;
  • 61 041 321 ÷ 2 = 30 520 660 + 1;
  • 30 520 660 ÷ 2 = 15 260 330 + 0;
  • 15 260 330 ÷ 2 = 7 630 165 + 0;
  • 7 630 165 ÷ 2 = 3 815 082 + 1;
  • 3 815 082 ÷ 2 = 1 907 541 + 0;
  • 1 907 541 ÷ 2 = 953 770 + 1;
  • 953 770 ÷ 2 = 476 885 + 0;
  • 476 885 ÷ 2 = 238 442 + 1;
  • 238 442 ÷ 2 = 119 221 + 0;
  • 119 221 ÷ 2 = 59 610 + 1;
  • 59 610 ÷ 2 = 29 805 + 0;
  • 29 805 ÷ 2 = 14 902 + 1;
  • 14 902 ÷ 2 = 7 451 + 0;
  • 7 451 ÷ 2 = 3 725 + 1;
  • 3 725 ÷ 2 = 1 862 + 1;
  • 1 862 ÷ 2 = 931 + 0;
  • 931 ÷ 2 = 465 + 1;
  • 465 ÷ 2 = 232 + 1;
  • 232 ÷ 2 = 116 + 0;
  • 116 ÷ 2 = 58 + 0;
  • 58 ÷ 2 = 29 + 0;
  • 29 ÷ 2 = 14 + 1;
  • 14 ÷ 2 = 7 + 0;
  • 7 ÷ 2 = 3 + 1;
  • 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.


1 000 101 009 959(10) = 1110 1000 1101 1010 1010 1010 0101 1010 0010 0111(2)


3. Determine the signed binary number bit length:

The base 2 number's actual length, in bits: 40.

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, 40,

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 1 000 101 009 959(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:

1 000 101 009 959(10) = 0000 0000 0000 0000 0000 0000 1110 1000 1101 1010 1010 1010 0101 1010 0010 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 1 000 101 009 958 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 1 000 101 009 960 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