Signed: Integer ↗ Binary: -109 209 807 510 Convert the Integer Number to a Signed Binary. Converting and Writing the Base Ten Decimal System Signed Integer as Binary Code (Written in Base Two)

Signed integer number -109 209 807 510(10)
converted and written as a signed binary (base 2) = ?

1. Start with the positive version of the number:

|-109 209 807 510| = 109 209 807 510

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;
  • 109 209 807 510 ÷ 2 = 54 604 903 755 + 0;
  • 54 604 903 755 ÷ 2 = 27 302 451 877 + 1;
  • 27 302 451 877 ÷ 2 = 13 651 225 938 + 1;
  • 13 651 225 938 ÷ 2 = 6 825 612 969 + 0;
  • 6 825 612 969 ÷ 2 = 3 412 806 484 + 1;
  • 3 412 806 484 ÷ 2 = 1 706 403 242 + 0;
  • 1 706 403 242 ÷ 2 = 853 201 621 + 0;
  • 853 201 621 ÷ 2 = 426 600 810 + 1;
  • 426 600 810 ÷ 2 = 213 300 405 + 0;
  • 213 300 405 ÷ 2 = 106 650 202 + 1;
  • 106 650 202 ÷ 2 = 53 325 101 + 0;
  • 53 325 101 ÷ 2 = 26 662 550 + 1;
  • 26 662 550 ÷ 2 = 13 331 275 + 0;
  • 13 331 275 ÷ 2 = 6 665 637 + 1;
  • 6 665 637 ÷ 2 = 3 332 818 + 1;
  • 3 332 818 ÷ 2 = 1 666 409 + 0;
  • 1 666 409 ÷ 2 = 833 204 + 1;
  • 833 204 ÷ 2 = 416 602 + 0;
  • 416 602 ÷ 2 = 208 301 + 0;
  • 208 301 ÷ 2 = 104 150 + 1;
  • 104 150 ÷ 2 = 52 075 + 0;
  • 52 075 ÷ 2 = 26 037 + 1;
  • 26 037 ÷ 2 = 13 018 + 1;
  • 13 018 ÷ 2 = 6 509 + 0;
  • 6 509 ÷ 2 = 3 254 + 1;
  • 3 254 ÷ 2 = 1 627 + 0;
  • 1 627 ÷ 2 = 813 + 1;
  • 813 ÷ 2 = 406 + 1;
  • 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.


109 209 807 510(10) = 1 1001 0110 1101 0110 1001 0110 1010 1001 0110(2)


4. 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) 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, 37,

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:


109 209 807 510(10) = 0000 0000 0000 0000 0000 0000 0001 1001 0110 1101 0110 1001 0110 1010 1001 0110


6. Get the negative integer number representation:

To get the negative integer number representation on 64 bits (8 Bytes),

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


Number -109 209 807 510(10), a signed integer number (with sign),
converted from decimal system (from base 10)
and written as a signed binary (in base 2):

-109 209 807 510(10) = 1000 0000 0000 0000 0000 0000 0001 1001 0110 1101 0110 1001 0110 1010 1001 0110

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

More operations on signed integer numbers:

» Signed integer number -109 209 807 511 converted from decimal system (from base 10) and written as a signed binary (in base 2) = ?

» Signed integer number -109 209 807 509 converted from decimal system (from base 10) and written as a signed binary (in base 2) = ?

The latest signed integer numbers (that are written in decimal system, in base ten) converted and written as signed binary numbers

Convert the base ten decimal system integer number 29,012,010, write it as a signed binary written in base two Apr 30 18:50 UTC (GMT)
Convert the base ten decimal system integer number 1,967,021, write it as a signed binary written in base two Apr 30 18:50 UTC (GMT)
Convert the base ten decimal system integer number -846,706,851, write it as a signed binary written in base two Apr 30 18:50 UTC (GMT)
Convert the base ten decimal system integer number -333,341, write it as a signed binary written in base two Apr 30 18:50 UTC (GMT)
Convert the base ten decimal system integer number 17,112,012, write it as a signed binary written in base two Apr 30 18:50 UTC (GMT)
Convert the base ten decimal system integer number 21,122,017, write it as a signed binary written in base two Apr 30 18:50 UTC (GMT)
Convert the base ten decimal system integer number 17,014, write it as a signed binary written in base two Apr 30 18:50 UTC (GMT)
Convert the base ten decimal system integer number 234,567,890,925, write it as a signed binary written in base two Apr 30 18:50 UTC (GMT)
Convert the base ten decimal system integer number 1,011,111,125, write it as a signed binary written in base two Apr 30 18:50 UTC (GMT)
Convert the base ten decimal system integer number 80,094, write it as a signed binary written in base two Apr 30 18:50 UTC (GMT)
All the decimal system integer numbers (written in base ten) converted and written as signed binary numbers

How to convert signed integers from decimal system 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