Convert -6 917 528 876 943 091 035 to a Signed Binary (Base 2)

How to convert -6 917 528 876 943 091 035(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 -6 917 528 876 943 091 035 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:

|-6 917 528 876 943 091 035| = 6 917 528 876 943 091 035

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;
  • 6 917 528 876 943 091 035 ÷ 2 = 3 458 764 438 471 545 517 + 1;
  • 3 458 764 438 471 545 517 ÷ 2 = 1 729 382 219 235 772 758 + 1;
  • 1 729 382 219 235 772 758 ÷ 2 = 864 691 109 617 886 379 + 0;
  • 864 691 109 617 886 379 ÷ 2 = 432 345 554 808 943 189 + 1;
  • 432 345 554 808 943 189 ÷ 2 = 216 172 777 404 471 594 + 1;
  • 216 172 777 404 471 594 ÷ 2 = 108 086 388 702 235 797 + 0;
  • 108 086 388 702 235 797 ÷ 2 = 54 043 194 351 117 898 + 1;
  • 54 043 194 351 117 898 ÷ 2 = 27 021 597 175 558 949 + 0;
  • 27 021 597 175 558 949 ÷ 2 = 13 510 798 587 779 474 + 1;
  • 13 510 798 587 779 474 ÷ 2 = 6 755 399 293 889 737 + 0;
  • 6 755 399 293 889 737 ÷ 2 = 3 377 699 646 944 868 + 1;
  • 3 377 699 646 944 868 ÷ 2 = 1 688 849 823 472 434 + 0;
  • 1 688 849 823 472 434 ÷ 2 = 844 424 911 736 217 + 0;
  • 844 424 911 736 217 ÷ 2 = 422 212 455 868 108 + 1;
  • 422 212 455 868 108 ÷ 2 = 211 106 227 934 054 + 0;
  • 211 106 227 934 054 ÷ 2 = 105 553 113 967 027 + 0;
  • 105 553 113 967 027 ÷ 2 = 52 776 556 983 513 + 1;
  • 52 776 556 983 513 ÷ 2 = 26 388 278 491 756 + 1;
  • 26 388 278 491 756 ÷ 2 = 13 194 139 245 878 + 0;
  • 13 194 139 245 878 ÷ 2 = 6 597 069 622 939 + 0;
  • 6 597 069 622 939 ÷ 2 = 3 298 534 811 469 + 1;
  • 3 298 534 811 469 ÷ 2 = 1 649 267 405 734 + 1;
  • 1 649 267 405 734 ÷ 2 = 824 633 702 867 + 0;
  • 824 633 702 867 ÷ 2 = 412 316 851 433 + 1;
  • 412 316 851 433 ÷ 2 = 206 158 425 716 + 1;
  • 206 158 425 716 ÷ 2 = 103 079 212 858 + 0;
  • 103 079 212 858 ÷ 2 = 51 539 606 429 + 0;
  • 51 539 606 429 ÷ 2 = 25 769 803 214 + 1;
  • 25 769 803 214 ÷ 2 = 12 884 901 607 + 0;
  • 12 884 901 607 ÷ 2 = 6 442 450 803 + 1;
  • 6 442 450 803 ÷ 2 = 3 221 225 401 + 1;
  • 3 221 225 401 ÷ 2 = 1 610 612 700 + 1;
  • 1 610 612 700 ÷ 2 = 805 306 350 + 0;
  • 805 306 350 ÷ 2 = 402 653 175 + 0;
  • 402 653 175 ÷ 2 = 201 326 587 + 1;
  • 201 326 587 ÷ 2 = 100 663 293 + 1;
  • 100 663 293 ÷ 2 = 50 331 646 + 1;
  • 50 331 646 ÷ 2 = 25 165 823 + 0;
  • 25 165 823 ÷ 2 = 12 582 911 + 1;
  • 12 582 911 ÷ 2 = 6 291 455 + 1;
  • 6 291 455 ÷ 2 = 3 145 727 + 1;
  • 3 145 727 ÷ 2 = 1 572 863 + 1;
  • 1 572 863 ÷ 2 = 786 431 + 1;
  • 786 431 ÷ 2 = 393 215 + 1;
  • 393 215 ÷ 2 = 196 607 + 1;
  • 196 607 ÷ 2 = 98 303 + 1;
  • 98 303 ÷ 2 = 49 151 + 1;
  • 49 151 ÷ 2 = 24 575 + 1;
  • 24 575 ÷ 2 = 12 287 + 1;
  • 12 287 ÷ 2 = 6 143 + 1;
  • 6 143 ÷ 2 = 3 071 + 1;
  • 3 071 ÷ 2 = 1 535 + 1;
  • 1 535 ÷ 2 = 767 + 1;
  • 767 ÷ 2 = 383 + 1;
  • 383 ÷ 2 = 191 + 1;
  • 191 ÷ 2 = 95 + 1;
  • 95 ÷ 2 = 47 + 1;
  • 47 ÷ 2 = 23 + 1;
  • 23 ÷ 2 = 11 + 1;
  • 11 ÷ 2 = 5 + 1;
  • 5 ÷ 2 = 2 + 1;
  • 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.

6 917 528 876 943 091 035(10) = 101 1111 1111 1111 1111 1111 1101 1100 1110 1001 1011 0011 0010 0101 0101 1011(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:


6 917 528 876 943 091 035(10) = 0101 1111 1111 1111 1111 1111 1101 1100 1110 1001 1011 0011 0010 0101 0101 1011

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...


-6 917 528 876 943 091 035(10) Base 10 integer number converted and written as a signed binary code (in base 2):

-6 917 528 876 943 091 035(10) = 1101 1111 1111 1111 1111 1111 1101 1100 1110 1001 1011 0011 0010 0101 0101 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