Convert -14 234 932 494 215 to a Signed Binary (Base 2)

How to convert -14 234 932 494 215(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 -14 234 932 494 215 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:

|-14 234 932 494 215| = 14 234 932 494 215

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;
  • 14 234 932 494 215 ÷ 2 = 7 117 466 247 107 + 1;
  • 7 117 466 247 107 ÷ 2 = 3 558 733 123 553 + 1;
  • 3 558 733 123 553 ÷ 2 = 1 779 366 561 776 + 1;
  • 1 779 366 561 776 ÷ 2 = 889 683 280 888 + 0;
  • 889 683 280 888 ÷ 2 = 444 841 640 444 + 0;
  • 444 841 640 444 ÷ 2 = 222 420 820 222 + 0;
  • 222 420 820 222 ÷ 2 = 111 210 410 111 + 0;
  • 111 210 410 111 ÷ 2 = 55 605 205 055 + 1;
  • 55 605 205 055 ÷ 2 = 27 802 602 527 + 1;
  • 27 802 602 527 ÷ 2 = 13 901 301 263 + 1;
  • 13 901 301 263 ÷ 2 = 6 950 650 631 + 1;
  • 6 950 650 631 ÷ 2 = 3 475 325 315 + 1;
  • 3 475 325 315 ÷ 2 = 1 737 662 657 + 1;
  • 1 737 662 657 ÷ 2 = 868 831 328 + 1;
  • 868 831 328 ÷ 2 = 434 415 664 + 0;
  • 434 415 664 ÷ 2 = 217 207 832 + 0;
  • 217 207 832 ÷ 2 = 108 603 916 + 0;
  • 108 603 916 ÷ 2 = 54 301 958 + 0;
  • 54 301 958 ÷ 2 = 27 150 979 + 0;
  • 27 150 979 ÷ 2 = 13 575 489 + 1;
  • 13 575 489 ÷ 2 = 6 787 744 + 1;
  • 6 787 744 ÷ 2 = 3 393 872 + 0;
  • 3 393 872 ÷ 2 = 1 696 936 + 0;
  • 1 696 936 ÷ 2 = 848 468 + 0;
  • 848 468 ÷ 2 = 424 234 + 0;
  • 424 234 ÷ 2 = 212 117 + 0;
  • 212 117 ÷ 2 = 106 058 + 1;
  • 106 058 ÷ 2 = 53 029 + 0;
  • 53 029 ÷ 2 = 26 514 + 1;
  • 26 514 ÷ 2 = 13 257 + 0;
  • 13 257 ÷ 2 = 6 628 + 1;
  • 6 628 ÷ 2 = 3 314 + 0;
  • 3 314 ÷ 2 = 1 657 + 0;
  • 1 657 ÷ 2 = 828 + 1;
  • 828 ÷ 2 = 414 + 0;
  • 414 ÷ 2 = 207 + 0;
  • 207 ÷ 2 = 103 + 1;
  • 103 ÷ 2 = 51 + 1;
  • 51 ÷ 2 = 25 + 1;
  • 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.

14 234 932 494 215(10) = 1100 1111 0010 0101 0100 0001 1000 0011 1111 1000 0111(2)


4. Determine the signed binary number bit length:

  • The base 2 number's actual length, in bits: 44.

  • 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, 44,

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:


14 234 932 494 215(10) = 0000 0000 0000 0000 0000 1100 1111 0010 0101 0100 0001 1000 0011 1111 1000 0111

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...


-14 234 932 494 215(10) Base 10 integer number converted and written as a signed binary code (in base 2):

-14 234 932 494 215(10) = 1000 0000 0000 0000 0000 1100 1111 0010 0101 0100 0001 1000 0011 1111 1000 0111

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