Convert -8 441 850 790 118 254 670 to a Signed Binary (Base 2)

How to convert -8 441 850 790 118 254 670(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 -8 441 850 790 118 254 670 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:

|-8 441 850 790 118 254 670| = 8 441 850 790 118 254 670

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;
  • 8 441 850 790 118 254 670 ÷ 2 = 4 220 925 395 059 127 335 + 0;
  • 4 220 925 395 059 127 335 ÷ 2 = 2 110 462 697 529 563 667 + 1;
  • 2 110 462 697 529 563 667 ÷ 2 = 1 055 231 348 764 781 833 + 1;
  • 1 055 231 348 764 781 833 ÷ 2 = 527 615 674 382 390 916 + 1;
  • 527 615 674 382 390 916 ÷ 2 = 263 807 837 191 195 458 + 0;
  • 263 807 837 191 195 458 ÷ 2 = 131 903 918 595 597 729 + 0;
  • 131 903 918 595 597 729 ÷ 2 = 65 951 959 297 798 864 + 1;
  • 65 951 959 297 798 864 ÷ 2 = 32 975 979 648 899 432 + 0;
  • 32 975 979 648 899 432 ÷ 2 = 16 487 989 824 449 716 + 0;
  • 16 487 989 824 449 716 ÷ 2 = 8 243 994 912 224 858 + 0;
  • 8 243 994 912 224 858 ÷ 2 = 4 121 997 456 112 429 + 0;
  • 4 121 997 456 112 429 ÷ 2 = 2 060 998 728 056 214 + 1;
  • 2 060 998 728 056 214 ÷ 2 = 1 030 499 364 028 107 + 0;
  • 1 030 499 364 028 107 ÷ 2 = 515 249 682 014 053 + 1;
  • 515 249 682 014 053 ÷ 2 = 257 624 841 007 026 + 1;
  • 257 624 841 007 026 ÷ 2 = 128 812 420 503 513 + 0;
  • 128 812 420 503 513 ÷ 2 = 64 406 210 251 756 + 1;
  • 64 406 210 251 756 ÷ 2 = 32 203 105 125 878 + 0;
  • 32 203 105 125 878 ÷ 2 = 16 101 552 562 939 + 0;
  • 16 101 552 562 939 ÷ 2 = 8 050 776 281 469 + 1;
  • 8 050 776 281 469 ÷ 2 = 4 025 388 140 734 + 1;
  • 4 025 388 140 734 ÷ 2 = 2 012 694 070 367 + 0;
  • 2 012 694 070 367 ÷ 2 = 1 006 347 035 183 + 1;
  • 1 006 347 035 183 ÷ 2 = 503 173 517 591 + 1;
  • 503 173 517 591 ÷ 2 = 251 586 758 795 + 1;
  • 251 586 758 795 ÷ 2 = 125 793 379 397 + 1;
  • 125 793 379 397 ÷ 2 = 62 896 689 698 + 1;
  • 62 896 689 698 ÷ 2 = 31 448 344 849 + 0;
  • 31 448 344 849 ÷ 2 = 15 724 172 424 + 1;
  • 15 724 172 424 ÷ 2 = 7 862 086 212 + 0;
  • 7 862 086 212 ÷ 2 = 3 931 043 106 + 0;
  • 3 931 043 106 ÷ 2 = 1 965 521 553 + 0;
  • 1 965 521 553 ÷ 2 = 982 760 776 + 1;
  • 982 760 776 ÷ 2 = 491 380 388 + 0;
  • 491 380 388 ÷ 2 = 245 690 194 + 0;
  • 245 690 194 ÷ 2 = 122 845 097 + 0;
  • 122 845 097 ÷ 2 = 61 422 548 + 1;
  • 61 422 548 ÷ 2 = 30 711 274 + 0;
  • 30 711 274 ÷ 2 = 15 355 637 + 0;
  • 15 355 637 ÷ 2 = 7 677 818 + 1;
  • 7 677 818 ÷ 2 = 3 838 909 + 0;
  • 3 838 909 ÷ 2 = 1 919 454 + 1;
  • 1 919 454 ÷ 2 = 959 727 + 0;
  • 959 727 ÷ 2 = 479 863 + 1;
  • 479 863 ÷ 2 = 239 931 + 1;
  • 239 931 ÷ 2 = 119 965 + 1;
  • 119 965 ÷ 2 = 59 982 + 1;
  • 59 982 ÷ 2 = 29 991 + 0;
  • 29 991 ÷ 2 = 14 995 + 1;
  • 14 995 ÷ 2 = 7 497 + 1;
  • 7 497 ÷ 2 = 3 748 + 1;
  • 3 748 ÷ 2 = 1 874 + 0;
  • 1 874 ÷ 2 = 937 + 0;
  • 937 ÷ 2 = 468 + 1;
  • 468 ÷ 2 = 234 + 0;
  • 234 ÷ 2 = 117 + 0;
  • 117 ÷ 2 = 58 + 1;
  • 58 ÷ 2 = 29 + 0;
  • 29 ÷ 2 = 14 + 1;
  • 14 ÷ 2 = 7 + 0;
  • 7 ÷ 2 = 3 + 1;
  • 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.

8 441 850 790 118 254 670(10) = 111 0101 0010 0111 0111 1010 1001 0001 0001 0111 1101 1001 0110 1000 0100 1110(2)


4. Determine the signed binary number bit length:

  • The base 2 number's actual length, in bits: 63.

  • 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, 63,

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:


8 441 850 790 118 254 670(10) = 0111 0101 0010 0111 0111 1010 1001 0001 0001 0111 1101 1001 0110 1000 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...


-8 441 850 790 118 254 670(10) Base 10 integer number converted and written as a signed binary code (in base 2):

-8 441 850 790 118 254 670(10) = 1111 0101 0010 0111 0111 1010 1001 0001 0001 0111 1101 1001 0110 1000 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