Integer to One's Complement Binary: Number 1 011 000 011 110 179 Converted and Written as a Signed Binary in One's Complement Representation

Integer number 1 011 000 011 110 179(10) written as a signed binary in one's complement representation

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;
  • 1 011 000 011 110 179 ÷ 2 = 505 500 005 555 089 + 1;
  • 505 500 005 555 089 ÷ 2 = 252 750 002 777 544 + 1;
  • 252 750 002 777 544 ÷ 2 = 126 375 001 388 772 + 0;
  • 126 375 001 388 772 ÷ 2 = 63 187 500 694 386 + 0;
  • 63 187 500 694 386 ÷ 2 = 31 593 750 347 193 + 0;
  • 31 593 750 347 193 ÷ 2 = 15 796 875 173 596 + 1;
  • 15 796 875 173 596 ÷ 2 = 7 898 437 586 798 + 0;
  • 7 898 437 586 798 ÷ 2 = 3 949 218 793 399 + 0;
  • 3 949 218 793 399 ÷ 2 = 1 974 609 396 699 + 1;
  • 1 974 609 396 699 ÷ 2 = 987 304 698 349 + 1;
  • 987 304 698 349 ÷ 2 = 493 652 349 174 + 1;
  • 493 652 349 174 ÷ 2 = 246 826 174 587 + 0;
  • 246 826 174 587 ÷ 2 = 123 413 087 293 + 1;
  • 123 413 087 293 ÷ 2 = 61 706 543 646 + 1;
  • 61 706 543 646 ÷ 2 = 30 853 271 823 + 0;
  • 30 853 271 823 ÷ 2 = 15 426 635 911 + 1;
  • 15 426 635 911 ÷ 2 = 7 713 317 955 + 1;
  • 7 713 317 955 ÷ 2 = 3 856 658 977 + 1;
  • 3 856 658 977 ÷ 2 = 1 928 329 488 + 1;
  • 1 928 329 488 ÷ 2 = 964 164 744 + 0;
  • 964 164 744 ÷ 2 = 482 082 372 + 0;
  • 482 082 372 ÷ 2 = 241 041 186 + 0;
  • 241 041 186 ÷ 2 = 120 520 593 + 0;
  • 120 520 593 ÷ 2 = 60 260 296 + 1;
  • 60 260 296 ÷ 2 = 30 130 148 + 0;
  • 30 130 148 ÷ 2 = 15 065 074 + 0;
  • 15 065 074 ÷ 2 = 7 532 537 + 0;
  • 7 532 537 ÷ 2 = 3 766 268 + 1;
  • 3 766 268 ÷ 2 = 1 883 134 + 0;
  • 1 883 134 ÷ 2 = 941 567 + 0;
  • 941 567 ÷ 2 = 470 783 + 1;
  • 470 783 ÷ 2 = 235 391 + 1;
  • 235 391 ÷ 2 = 117 695 + 1;
  • 117 695 ÷ 2 = 58 847 + 1;
  • 58 847 ÷ 2 = 29 423 + 1;
  • 29 423 ÷ 2 = 14 711 + 1;
  • 14 711 ÷ 2 = 7 355 + 1;
  • 7 355 ÷ 2 = 3 677 + 1;
  • 3 677 ÷ 2 = 1 838 + 1;
  • 1 838 ÷ 2 = 919 + 0;
  • 919 ÷ 2 = 459 + 1;
  • 459 ÷ 2 = 229 + 1;
  • 229 ÷ 2 = 114 + 1;
  • 114 ÷ 2 = 57 + 0;
  • 57 ÷ 2 = 28 + 1;
  • 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.


1 011 000 011 110 179(10) = 11 1001 0111 0111 1111 1100 1000 1000 0111 1011 0111 0010 0011(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 1 011 000 011 110 179(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:

1 011 000 011 110 179(10) = 0000 0000 0000 0011 1001 0111 0111 1111 1100 1000 1000 0111 1011 0111 0010 0011

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

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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