Convert -487 393 651 993 166 to a Signed Binary (Base 2)

How to convert -487 393 651 993 166(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 -487 393 651 993 166 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:

|-487 393 651 993 166| = 487 393 651 993 166

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;
  • 487 393 651 993 166 ÷ 2 = 243 696 825 996 583 + 0;
  • 243 696 825 996 583 ÷ 2 = 121 848 412 998 291 + 1;
  • 121 848 412 998 291 ÷ 2 = 60 924 206 499 145 + 1;
  • 60 924 206 499 145 ÷ 2 = 30 462 103 249 572 + 1;
  • 30 462 103 249 572 ÷ 2 = 15 231 051 624 786 + 0;
  • 15 231 051 624 786 ÷ 2 = 7 615 525 812 393 + 0;
  • 7 615 525 812 393 ÷ 2 = 3 807 762 906 196 + 1;
  • 3 807 762 906 196 ÷ 2 = 1 903 881 453 098 + 0;
  • 1 903 881 453 098 ÷ 2 = 951 940 726 549 + 0;
  • 951 940 726 549 ÷ 2 = 475 970 363 274 + 1;
  • 475 970 363 274 ÷ 2 = 237 985 181 637 + 0;
  • 237 985 181 637 ÷ 2 = 118 992 590 818 + 1;
  • 118 992 590 818 ÷ 2 = 59 496 295 409 + 0;
  • 59 496 295 409 ÷ 2 = 29 748 147 704 + 1;
  • 29 748 147 704 ÷ 2 = 14 874 073 852 + 0;
  • 14 874 073 852 ÷ 2 = 7 437 036 926 + 0;
  • 7 437 036 926 ÷ 2 = 3 718 518 463 + 0;
  • 3 718 518 463 ÷ 2 = 1 859 259 231 + 1;
  • 1 859 259 231 ÷ 2 = 929 629 615 + 1;
  • 929 629 615 ÷ 2 = 464 814 807 + 1;
  • 464 814 807 ÷ 2 = 232 407 403 + 1;
  • 232 407 403 ÷ 2 = 116 203 701 + 1;
  • 116 203 701 ÷ 2 = 58 101 850 + 1;
  • 58 101 850 ÷ 2 = 29 050 925 + 0;
  • 29 050 925 ÷ 2 = 14 525 462 + 1;
  • 14 525 462 ÷ 2 = 7 262 731 + 0;
  • 7 262 731 ÷ 2 = 3 631 365 + 1;
  • 3 631 365 ÷ 2 = 1 815 682 + 1;
  • 1 815 682 ÷ 2 = 907 841 + 0;
  • 907 841 ÷ 2 = 453 920 + 1;
  • 453 920 ÷ 2 = 226 960 + 0;
  • 226 960 ÷ 2 = 113 480 + 0;
  • 113 480 ÷ 2 = 56 740 + 0;
  • 56 740 ÷ 2 = 28 370 + 0;
  • 28 370 ÷ 2 = 14 185 + 0;
  • 14 185 ÷ 2 = 7 092 + 1;
  • 7 092 ÷ 2 = 3 546 + 0;
  • 3 546 ÷ 2 = 1 773 + 0;
  • 1 773 ÷ 2 = 886 + 1;
  • 886 ÷ 2 = 443 + 0;
  • 443 ÷ 2 = 221 + 1;
  • 221 ÷ 2 = 110 + 1;
  • 110 ÷ 2 = 55 + 0;
  • 55 ÷ 2 = 27 + 1;
  • 27 ÷ 2 = 13 + 1;
  • 13 ÷ 2 = 6 + 1;
  • 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.

487 393 651 993 166(10) = 1 1011 1011 0100 1000 0010 1101 0111 1110 0010 1010 0100 1110(2)


4. Determine the signed binary number bit length:

  • The base 2 number's actual length, in bits: 49.

  • 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, 49,

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:


487 393 651 993 166(10) = 0000 0000 0000 0001 1011 1011 0100 1000 0010 1101 0111 1110 0010 1010 0100 1110

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...


-487 393 651 993 166(10) Base 10 integer number converted and written as a signed binary code (in base 2):

-487 393 651 993 166(10) = 1000 0000 0000 0001 1011 1011 0100 1000 0010 1101 0111 1110 0010 1010 0100 1110

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