One's Complement: Integer ↗ Binary: 85 084 069 035 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 85 084 069 035(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;
  • 85 084 069 035 ÷ 2 = 42 542 034 517 + 1;
  • 42 542 034 517 ÷ 2 = 21 271 017 258 + 1;
  • 21 271 017 258 ÷ 2 = 10 635 508 629 + 0;
  • 10 635 508 629 ÷ 2 = 5 317 754 314 + 1;
  • 5 317 754 314 ÷ 2 = 2 658 877 157 + 0;
  • 2 658 877 157 ÷ 2 = 1 329 438 578 + 1;
  • 1 329 438 578 ÷ 2 = 664 719 289 + 0;
  • 664 719 289 ÷ 2 = 332 359 644 + 1;
  • 332 359 644 ÷ 2 = 166 179 822 + 0;
  • 166 179 822 ÷ 2 = 83 089 911 + 0;
  • 83 089 911 ÷ 2 = 41 544 955 + 1;
  • 41 544 955 ÷ 2 = 20 772 477 + 1;
  • 20 772 477 ÷ 2 = 10 386 238 + 1;
  • 10 386 238 ÷ 2 = 5 193 119 + 0;
  • 5 193 119 ÷ 2 = 2 596 559 + 1;
  • 2 596 559 ÷ 2 = 1 298 279 + 1;
  • 1 298 279 ÷ 2 = 649 139 + 1;
  • 649 139 ÷ 2 = 324 569 + 1;
  • 324 569 ÷ 2 = 162 284 + 1;
  • 162 284 ÷ 2 = 81 142 + 0;
  • 81 142 ÷ 2 = 40 571 + 0;
  • 40 571 ÷ 2 = 20 285 + 1;
  • 20 285 ÷ 2 = 10 142 + 1;
  • 10 142 ÷ 2 = 5 071 + 0;
  • 5 071 ÷ 2 = 2 535 + 1;
  • 2 535 ÷ 2 = 1 267 + 1;
  • 1 267 ÷ 2 = 633 + 1;
  • 633 ÷ 2 = 316 + 1;
  • 316 ÷ 2 = 158 + 0;
  • 158 ÷ 2 = 79 + 0;
  • 79 ÷ 2 = 39 + 1;
  • 39 ÷ 2 = 19 + 1;
  • 19 ÷ 2 = 9 + 1;
  • 9 ÷ 2 = 4 + 1;
  • 4 ÷ 2 = 2 + 0;
  • 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.


85 084 069 035(10) = 1 0011 1100 1111 0110 0111 1101 1100 1010 1011(2)


3. Determine the signed binary number bit length:

The base 2 number's actual length, in bits: 37.

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, 37,

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 85 084 069 035(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:

85 084 069 035(10) = 0000 0000 0000 0000 0000 0000 0001 0011 1100 1111 0110 0111 1101 1100 1010 1011

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 85 084 069 034 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 85 084 069 036 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