Convert -111 691 709 001 545 to a Signed Binary in One's (1's) Complement Representation

How to convert decimal number -111 691 709 001 545(10) to a signed binary in one's (1's) complement representation

What are the steps to convert decimal number
-111 691 709 001 545 to a signed binary in one's (1's) complement representation?

  • A signed integer, written in base ten, or a decimal system number, is a number written using the digits 0 through 9 and the sign, which can be positive (+) or negative (-). If positive, the sign is usually not written. A number written in base two, or binary, is a number written using only the digits 0 and 1.

1. Start with the positive version of the number:

|-111 691 709 001 545| = 111 691 709 001 545

2. Divide the number repeatedly by 2:

Keep track of each remainder.

Stop when you get a quotient that is equal to zero.


  • division = quotient + remainder;
  • 111 691 709 001 545 ÷ 2 = 55 845 854 500 772 + 1;
  • 55 845 854 500 772 ÷ 2 = 27 922 927 250 386 + 0;
  • 27 922 927 250 386 ÷ 2 = 13 961 463 625 193 + 0;
  • 13 961 463 625 193 ÷ 2 = 6 980 731 812 596 + 1;
  • 6 980 731 812 596 ÷ 2 = 3 490 365 906 298 + 0;
  • 3 490 365 906 298 ÷ 2 = 1 745 182 953 149 + 0;
  • 1 745 182 953 149 ÷ 2 = 872 591 476 574 + 1;
  • 872 591 476 574 ÷ 2 = 436 295 738 287 + 0;
  • 436 295 738 287 ÷ 2 = 218 147 869 143 + 1;
  • 218 147 869 143 ÷ 2 = 109 073 934 571 + 1;
  • 109 073 934 571 ÷ 2 = 54 536 967 285 + 1;
  • 54 536 967 285 ÷ 2 = 27 268 483 642 + 1;
  • 27 268 483 642 ÷ 2 = 13 634 241 821 + 0;
  • 13 634 241 821 ÷ 2 = 6 817 120 910 + 1;
  • 6 817 120 910 ÷ 2 = 3 408 560 455 + 0;
  • 3 408 560 455 ÷ 2 = 1 704 280 227 + 1;
  • 1 704 280 227 ÷ 2 = 852 140 113 + 1;
  • 852 140 113 ÷ 2 = 426 070 056 + 1;
  • 426 070 056 ÷ 2 = 213 035 028 + 0;
  • 213 035 028 ÷ 2 = 106 517 514 + 0;
  • 106 517 514 ÷ 2 = 53 258 757 + 0;
  • 53 258 757 ÷ 2 = 26 629 378 + 1;
  • 26 629 378 ÷ 2 = 13 314 689 + 0;
  • 13 314 689 ÷ 2 = 6 657 344 + 1;
  • 6 657 344 ÷ 2 = 3 328 672 + 0;
  • 3 328 672 ÷ 2 = 1 664 336 + 0;
  • 1 664 336 ÷ 2 = 832 168 + 0;
  • 832 168 ÷ 2 = 416 084 + 0;
  • 416 084 ÷ 2 = 208 042 + 0;
  • 208 042 ÷ 2 = 104 021 + 0;
  • 104 021 ÷ 2 = 52 010 + 1;
  • 52 010 ÷ 2 = 26 005 + 0;
  • 26 005 ÷ 2 = 13 002 + 1;
  • 13 002 ÷ 2 = 6 501 + 0;
  • 6 501 ÷ 2 = 3 250 + 1;
  • 3 250 ÷ 2 = 1 625 + 0;
  • 1 625 ÷ 2 = 812 + 1;
  • 812 ÷ 2 = 406 + 0;
  • 406 ÷ 2 = 203 + 0;
  • 203 ÷ 2 = 101 + 1;
  • 101 ÷ 2 = 50 + 1;
  • 50 ÷ 2 = 25 + 0;
  • 25 ÷ 2 = 12 + 1;
  • 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:

Take all the remainders starting from the bottom of the list constructed above.

111 691 709 001 545(10) = 110 0101 1001 0101 0100 0000 1010 0011 1010 1111 0100 1001(2)

4. Determine the signed binary number bit length:

  • The base 2 number's actual length, in bits: 47.

  • 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, 47,

3) so that the first bit (leftmost) could be zero
(we deal with a positive number at this moment)

=== is: 64.


5. 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.


111 691 709 001 545(10) = 0000 0000 0000 0000 0110 0101 1001 0101 0100 0000 1010 0011 1010 1111 0100 1001

6. Get the negative integer number representation:

  • To write the negative integer number on 64 bits (8 Bytes), as a signed binary in one's complement representation,

  • ... Reverse all the bits from 0 to 1 and from 1 to 0 (flip the digits).


-111 691 709 001 545(10) = !(0000 0000 0000 0000 0110 0101 1001 0101 0100 0000 1010 0011 1010 1111 0100 1001)


Decimal Number -111 691 709 001 545(10) converted to signed binary in one's complement representation:

-111 691 709 001 545(10) = 1111 1111 1111 1111 1001 1010 0110 1010 1011 1111 0101 1100 0101 0000 1011 0110

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