Convert -1 094 795 483 to a Signed Binary (Base 2)

How to convert -1 094 795 483(10), a signed base 10 integer number? How to write it as a signed binary code in base 2

What are the required steps to convert base 10 integer
number -1 094 795 483 to signed binary code (in base 2)?

  • 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:

|-1 094 795 483| = 1 094 795 483

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;
  • 1 094 795 483 ÷ 2 = 547 397 741 + 1;
  • 547 397 741 ÷ 2 = 273 698 870 + 1;
  • 273 698 870 ÷ 2 = 136 849 435 + 0;
  • 136 849 435 ÷ 2 = 68 424 717 + 1;
  • 68 424 717 ÷ 2 = 34 212 358 + 1;
  • 34 212 358 ÷ 2 = 17 106 179 + 0;
  • 17 106 179 ÷ 2 = 8 553 089 + 1;
  • 8 553 089 ÷ 2 = 4 276 544 + 1;
  • 4 276 544 ÷ 2 = 2 138 272 + 0;
  • 2 138 272 ÷ 2 = 1 069 136 + 0;
  • 1 069 136 ÷ 2 = 534 568 + 0;
  • 534 568 ÷ 2 = 267 284 + 0;
  • 267 284 ÷ 2 = 133 642 + 0;
  • 133 642 ÷ 2 = 66 821 + 0;
  • 66 821 ÷ 2 = 33 410 + 1;
  • 33 410 ÷ 2 = 16 705 + 0;
  • 16 705 ÷ 2 = 8 352 + 1;
  • 8 352 ÷ 2 = 4 176 + 0;
  • 4 176 ÷ 2 = 2 088 + 0;
  • 2 088 ÷ 2 = 1 044 + 0;
  • 1 044 ÷ 2 = 522 + 0;
  • 522 ÷ 2 = 261 + 0;
  • 261 ÷ 2 = 130 + 1;
  • 130 ÷ 2 = 65 + 0;
  • 65 ÷ 2 = 32 + 1;
  • 32 ÷ 2 = 16 + 0;
  • 16 ÷ 2 = 8 + 0;
  • 8 ÷ 2 = 4 + 0;
  • 4 ÷ 2 = 2 + 0;
  • 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.

1 094 795 483(10) = 100 0001 0100 0001 0100 0000 1101 1011(2)


4. Determine the signed binary number bit length:

  • The base 2 number's actual length, in bits: 31.

  • 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) is reserved for 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, 31,

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:


1 094 795 483(10) = 0100 0001 0100 0001 0100 0000 1101 1011

6. Get the negative integer number representation:

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

... change the first bit (the leftmost), from 0 to 1...


-1 094 795 483(10) Base 10 integer number converted and written as a signed binary code (in base 2):

-1 094 795 483(10) = 1100 0001 0100 0001 0100 0000 1101 1011

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

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How to convert signed base 10 integers in decimal to binary code system

Follow the steps below to convert a signed base ten integer number to signed binary:

  • 1. In a signed binary, first bit (the leftmost) is reserved for sign: 0 = positive integer number, 1 = positive integer number. If the number to be converted is negative, start with its positive version.
  • 2. Divide repeatedly by 2 the positive integer number keeping track of each remainder. STOP when we get a quotient that is 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 have a length of 4, 8, 16, 32, 64, ... bits (power of 2) - if needed, fill in extra '0' bits in front of the base 2 number (to the left), up to the right length; this way the first bit (the leftmost one) is always '0', as for a positive representation.
  • 5. To get the negative reprezentation of the number, simply switch the first bit (the leftmost one), from '0' to '1'.

Example: convert the negative number -63 from decimal system (base ten) to signed binary code system:

  • 1. Start with the positive version of the number: |-63| = 63;
  • 2. Divide repeatedly 63 by 2, keeping track of each remainder, until we get a quotient that is equal to zero:
    • division = quotient + remainder
    • 63 ÷ 2 = 31 + 1
    • 31 ÷ 2 = 15 + 1
    • 15 ÷ 2 = 7 + 1
    • 7 ÷ 2 = 3 + 1
    • 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:
    63(10) = 11 1111(2)
  • 4. The actual length of base 2 representation number is 6, so the positive binary computer representation length of the signed binary will take in this case 8 bits (the least power of 2 higher than 6) - add extra '0's in front (to the left), up to the required length; this way the first bit (the leftmost one) is to be '0', as for a positive number:
    63(10) = 0011 1111(2)
  • 5. To get the negative integer number representation simply change the first bit (the leftmost), from '0' to '1':
    -63(10) = 1011 1111
  • Number -63(10), signed integer, converted from decimal system (base 10) to signed binary = 1011 1111