Integer to One's Complement Binary: Number -794 412 989 Converted and Written as a Signed Binary in One's Complement Representation

Integer number -794 412 989(10) written as a signed binary in one's complement representation

1. Start with the positive version of the number:

|-794 412 989| = 794 412 989

2. 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;
  • 794 412 989 ÷ 2 = 397 206 494 + 1;
  • 397 206 494 ÷ 2 = 198 603 247 + 0;
  • 198 603 247 ÷ 2 = 99 301 623 + 1;
  • 99 301 623 ÷ 2 = 49 650 811 + 1;
  • 49 650 811 ÷ 2 = 24 825 405 + 1;
  • 24 825 405 ÷ 2 = 12 412 702 + 1;
  • 12 412 702 ÷ 2 = 6 206 351 + 0;
  • 6 206 351 ÷ 2 = 3 103 175 + 1;
  • 3 103 175 ÷ 2 = 1 551 587 + 1;
  • 1 551 587 ÷ 2 = 775 793 + 1;
  • 775 793 ÷ 2 = 387 896 + 1;
  • 387 896 ÷ 2 = 193 948 + 0;
  • 193 948 ÷ 2 = 96 974 + 0;
  • 96 974 ÷ 2 = 48 487 + 0;
  • 48 487 ÷ 2 = 24 243 + 1;
  • 24 243 ÷ 2 = 12 121 + 1;
  • 12 121 ÷ 2 = 6 060 + 1;
  • 6 060 ÷ 2 = 3 030 + 0;
  • 3 030 ÷ 2 = 1 515 + 0;
  • 1 515 ÷ 2 = 757 + 1;
  • 757 ÷ 2 = 378 + 1;
  • 378 ÷ 2 = 189 + 0;
  • 189 ÷ 2 = 94 + 1;
  • 94 ÷ 2 = 47 + 0;
  • 47 ÷ 2 = 23 + 1;
  • 23 ÷ 2 = 11 + 1;
  • 11 ÷ 2 = 5 + 1;
  • 5 ÷ 2 = 2 + 1;
  • 2 ÷ 2 = 1 + 0;
  • 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.


794 412 989(10) = 10 1111 0101 1001 1100 0111 1011 1101(2)


4. Determine the signed binary number bit length:

The base 2 number's actual length, in bits: 30.

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, 30,

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

=== is: 32.


5. Get the positive binary computer representation on 32 bits (4 Bytes):

If needed, add extra 0s in front (to the left) of the base 2 number, up to the required length, 32.


794 412 989(10) = 0010 1111 0101 1001 1100 0111 1011 1101


6. Get the negative integer number representation:

To write the negative integer number on 32 bits (4 Bytes),

as a signed binary in one's complement representation,

... replace all the bits on 0 with 1s and all the bits set on 1 with 0s.


Reverse the digits, flip the digits:

Replace the bits set on 0 with 1s and the bits set on 1 with 0s.

-794 412 989(10) = !(0010 1111 0101 1001 1100 0111 1011 1101)


Number -794 412 989(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:

-794 412 989(10) = 1101 0000 1010 0110 0011 1000 0100 0010

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