One's Complement: Integer ↗ Binary: 2 782 928 897 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 2 782 928 897(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;
  • 2 782 928 897 ÷ 2 = 1 391 464 448 + 1;
  • 1 391 464 448 ÷ 2 = 695 732 224 + 0;
  • 695 732 224 ÷ 2 = 347 866 112 + 0;
  • 347 866 112 ÷ 2 = 173 933 056 + 0;
  • 173 933 056 ÷ 2 = 86 966 528 + 0;
  • 86 966 528 ÷ 2 = 43 483 264 + 0;
  • 43 483 264 ÷ 2 = 21 741 632 + 0;
  • 21 741 632 ÷ 2 = 10 870 816 + 0;
  • 10 870 816 ÷ 2 = 5 435 408 + 0;
  • 5 435 408 ÷ 2 = 2 717 704 + 0;
  • 2 717 704 ÷ 2 = 1 358 852 + 0;
  • 1 358 852 ÷ 2 = 679 426 + 0;
  • 679 426 ÷ 2 = 339 713 + 0;
  • 339 713 ÷ 2 = 169 856 + 1;
  • 169 856 ÷ 2 = 84 928 + 0;
  • 84 928 ÷ 2 = 42 464 + 0;
  • 42 464 ÷ 2 = 21 232 + 0;
  • 21 232 ÷ 2 = 10 616 + 0;
  • 10 616 ÷ 2 = 5 308 + 0;
  • 5 308 ÷ 2 = 2 654 + 0;
  • 2 654 ÷ 2 = 1 327 + 0;
  • 1 327 ÷ 2 = 663 + 1;
  • 663 ÷ 2 = 331 + 1;
  • 331 ÷ 2 = 165 + 1;
  • 165 ÷ 2 = 82 + 1;
  • 82 ÷ 2 = 41 + 0;
  • 41 ÷ 2 = 20 + 1;
  • 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.


2 782 928 897(10) = 1010 0101 1110 0000 0010 0000 0000 0001(2)


3. Determine the signed binary number bit length:

The base 2 number's actual length, in bits: 32.

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, 32,

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 2 782 928 897(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:

2 782 928 897(10) = 0000 0000 0000 0000 0000 0000 0000 0000 1010 0101 1110 0000 0010 0000 0000 0001

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 2 782 928 896 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 2 782 928 898 converted from decimal system (from base 10) and written as a signed binary in one's complement representation (written in base 2) = ?

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

Convert and write the decimal system (base 10) signed integer number -987,654,297 as a signed binary written in one's complement representation May 20 02:09 UTC (GMT)
Convert and write the decimal system (base 10) signed integer number -33,456,452 as a signed binary written in one's complement representation May 20 02:09 UTC (GMT)
Convert and write the decimal system (base 10) signed integer number 1,431,586,158 as a signed binary written in one's complement representation May 20 02:09 UTC (GMT)
Convert and write the decimal system (base 10) signed integer number 21,474,854 as a signed binary written in one's complement representation May 20 02:08 UTC (GMT)
Convert and write the decimal system (base 10) signed integer number 10,011,111,001,066 as a signed binary written in one's complement representation May 20 02:08 UTC (GMT)
Convert and write the decimal system (base 10) signed integer number 1,012,027 as a signed binary written in one's complement representation May 20 02:08 UTC (GMT)
Convert and write the decimal system (base 10) signed integer number -3,148 as a signed binary written in one's complement representation May 20 02:08 UTC (GMT)
Convert and write the decimal system (base 10) signed integer number 63 as a signed binary written in one's complement representation May 20 02:08 UTC (GMT)
Convert and write the decimal system (base 10) signed integer number 26,897 as a signed binary written in one's complement representation May 20 02:08 UTC (GMT)
Convert and write the decimal system (base 10) signed integer number -48,861 as a signed binary written in one's complement representation May 20 02:06 UTC (GMT)
All the decimal integer numbers converted and written as signed binary numbers 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