One's Complement: Integer ↗ Binary: 1 000 100 100 109 989 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 1 000 100 100 109 989(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;
  • 1 000 100 100 109 989 ÷ 2 = 500 050 050 054 994 + 1;
  • 500 050 050 054 994 ÷ 2 = 250 025 025 027 497 + 0;
  • 250 025 025 027 497 ÷ 2 = 125 012 512 513 748 + 1;
  • 125 012 512 513 748 ÷ 2 = 62 506 256 256 874 + 0;
  • 62 506 256 256 874 ÷ 2 = 31 253 128 128 437 + 0;
  • 31 253 128 128 437 ÷ 2 = 15 626 564 064 218 + 1;
  • 15 626 564 064 218 ÷ 2 = 7 813 282 032 109 + 0;
  • 7 813 282 032 109 ÷ 2 = 3 906 641 016 054 + 1;
  • 3 906 641 016 054 ÷ 2 = 1 953 320 508 027 + 0;
  • 1 953 320 508 027 ÷ 2 = 976 660 254 013 + 1;
  • 976 660 254 013 ÷ 2 = 488 330 127 006 + 1;
  • 488 330 127 006 ÷ 2 = 244 165 063 503 + 0;
  • 244 165 063 503 ÷ 2 = 122 082 531 751 + 1;
  • 122 082 531 751 ÷ 2 = 61 041 265 875 + 1;
  • 61 041 265 875 ÷ 2 = 30 520 632 937 + 1;
  • 30 520 632 937 ÷ 2 = 15 260 316 468 + 1;
  • 15 260 316 468 ÷ 2 = 7 630 158 234 + 0;
  • 7 630 158 234 ÷ 2 = 3 815 079 117 + 0;
  • 3 815 079 117 ÷ 2 = 1 907 539 558 + 1;
  • 1 907 539 558 ÷ 2 = 953 769 779 + 0;
  • 953 769 779 ÷ 2 = 476 884 889 + 1;
  • 476 884 889 ÷ 2 = 238 442 444 + 1;
  • 238 442 444 ÷ 2 = 119 221 222 + 0;
  • 119 221 222 ÷ 2 = 59 610 611 + 0;
  • 59 610 611 ÷ 2 = 29 805 305 + 1;
  • 29 805 305 ÷ 2 = 14 902 652 + 1;
  • 14 902 652 ÷ 2 = 7 451 326 + 0;
  • 7 451 326 ÷ 2 = 3 725 663 + 0;
  • 3 725 663 ÷ 2 = 1 862 831 + 1;
  • 1 862 831 ÷ 2 = 931 415 + 1;
  • 931 415 ÷ 2 = 465 707 + 1;
  • 465 707 ÷ 2 = 232 853 + 1;
  • 232 853 ÷ 2 = 116 426 + 1;
  • 116 426 ÷ 2 = 58 213 + 0;
  • 58 213 ÷ 2 = 29 106 + 1;
  • 29 106 ÷ 2 = 14 553 + 0;
  • 14 553 ÷ 2 = 7 276 + 1;
  • 7 276 ÷ 2 = 3 638 + 0;
  • 3 638 ÷ 2 = 1 819 + 0;
  • 1 819 ÷ 2 = 909 + 1;
  • 909 ÷ 2 = 454 + 1;
  • 454 ÷ 2 = 227 + 0;
  • 227 ÷ 2 = 113 + 1;
  • 113 ÷ 2 = 56 + 1;
  • 56 ÷ 2 = 28 + 0;
  • 28 ÷ 2 = 14 + 0;
  • 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.


1 000 100 100 109 989(10) = 11 1000 1101 1001 0101 1111 0011 0011 0100 1111 0110 1010 0101(2)


3. Determine the signed binary number bit length:

The base 2 number's actual length, in bits: 50.


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, 50,

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 1 000 100 100 109 989(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:

1 000 100 100 109 989(10) = 0000 0000 0000 0011 1000 1101 1001 0101 1111 0011 0011 0100 1111 0110 1010 0101

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

The latest signed integer numbers converted from decimal system (base ten) and written as signed binary in one's complement representation

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