Convert -6 937 650 605 005 805 061 to a Signed Binary (Base 2)

How to convert -6 937 650 605 005 805 061(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 -6 937 650 605 005 805 061 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:

|-6 937 650 605 005 805 061| = 6 937 650 605 005 805 061

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;
  • 6 937 650 605 005 805 061 ÷ 2 = 3 468 825 302 502 902 530 + 1;
  • 3 468 825 302 502 902 530 ÷ 2 = 1 734 412 651 251 451 265 + 0;
  • 1 734 412 651 251 451 265 ÷ 2 = 867 206 325 625 725 632 + 1;
  • 867 206 325 625 725 632 ÷ 2 = 433 603 162 812 862 816 + 0;
  • 433 603 162 812 862 816 ÷ 2 = 216 801 581 406 431 408 + 0;
  • 216 801 581 406 431 408 ÷ 2 = 108 400 790 703 215 704 + 0;
  • 108 400 790 703 215 704 ÷ 2 = 54 200 395 351 607 852 + 0;
  • 54 200 395 351 607 852 ÷ 2 = 27 100 197 675 803 926 + 0;
  • 27 100 197 675 803 926 ÷ 2 = 13 550 098 837 901 963 + 0;
  • 13 550 098 837 901 963 ÷ 2 = 6 775 049 418 950 981 + 1;
  • 6 775 049 418 950 981 ÷ 2 = 3 387 524 709 475 490 + 1;
  • 3 387 524 709 475 490 ÷ 2 = 1 693 762 354 737 745 + 0;
  • 1 693 762 354 737 745 ÷ 2 = 846 881 177 368 872 + 1;
  • 846 881 177 368 872 ÷ 2 = 423 440 588 684 436 + 0;
  • 423 440 588 684 436 ÷ 2 = 211 720 294 342 218 + 0;
  • 211 720 294 342 218 ÷ 2 = 105 860 147 171 109 + 0;
  • 105 860 147 171 109 ÷ 2 = 52 930 073 585 554 + 1;
  • 52 930 073 585 554 ÷ 2 = 26 465 036 792 777 + 0;
  • 26 465 036 792 777 ÷ 2 = 13 232 518 396 388 + 1;
  • 13 232 518 396 388 ÷ 2 = 6 616 259 198 194 + 0;
  • 6 616 259 198 194 ÷ 2 = 3 308 129 599 097 + 0;
  • 3 308 129 599 097 ÷ 2 = 1 654 064 799 548 + 1;
  • 1 654 064 799 548 ÷ 2 = 827 032 399 774 + 0;
  • 827 032 399 774 ÷ 2 = 413 516 199 887 + 0;
  • 413 516 199 887 ÷ 2 = 206 758 099 943 + 1;
  • 206 758 099 943 ÷ 2 = 103 379 049 971 + 1;
  • 103 379 049 971 ÷ 2 = 51 689 524 985 + 1;
  • 51 689 524 985 ÷ 2 = 25 844 762 492 + 1;
  • 25 844 762 492 ÷ 2 = 12 922 381 246 + 0;
  • 12 922 381 246 ÷ 2 = 6 461 190 623 + 0;
  • 6 461 190 623 ÷ 2 = 3 230 595 311 + 1;
  • 3 230 595 311 ÷ 2 = 1 615 297 655 + 1;
  • 1 615 297 655 ÷ 2 = 807 648 827 + 1;
  • 807 648 827 ÷ 2 = 403 824 413 + 1;
  • 403 824 413 ÷ 2 = 201 912 206 + 1;
  • 201 912 206 ÷ 2 = 100 956 103 + 0;
  • 100 956 103 ÷ 2 = 50 478 051 + 1;
  • 50 478 051 ÷ 2 = 25 239 025 + 1;
  • 25 239 025 ÷ 2 = 12 619 512 + 1;
  • 12 619 512 ÷ 2 = 6 309 756 + 0;
  • 6 309 756 ÷ 2 = 3 154 878 + 0;
  • 3 154 878 ÷ 2 = 1 577 439 + 0;
  • 1 577 439 ÷ 2 = 788 719 + 1;
  • 788 719 ÷ 2 = 394 359 + 1;
  • 394 359 ÷ 2 = 197 179 + 1;
  • 197 179 ÷ 2 = 98 589 + 1;
  • 98 589 ÷ 2 = 49 294 + 1;
  • 49 294 ÷ 2 = 24 647 + 0;
  • 24 647 ÷ 2 = 12 323 + 1;
  • 12 323 ÷ 2 = 6 161 + 1;
  • 6 161 ÷ 2 = 3 080 + 1;
  • 3 080 ÷ 2 = 1 540 + 0;
  • 1 540 ÷ 2 = 770 + 0;
  • 770 ÷ 2 = 385 + 0;
  • 385 ÷ 2 = 192 + 1;
  • 192 ÷ 2 = 96 + 0;
  • 96 ÷ 2 = 48 + 0;
  • 48 ÷ 2 = 24 + 0;
  • 24 ÷ 2 = 12 + 0;
  • 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.

6 937 650 605 005 805 061(10) = 110 0000 0100 0111 0111 1100 0111 0111 1100 1111 0010 0101 0001 0110 0000 0101(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:


6 937 650 605 005 805 061(10) = 0110 0000 0100 0111 0111 1100 0111 0111 1100 1111 0010 0101 0001 0110 0000 0101

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...


-6 937 650 605 005 805 061(10) Base 10 integer number converted and written as a signed binary code (in base 2):

-6 937 650 605 005 805 061(10) = 1110 0000 0100 0111 0111 1100 0111 0111 1100 1111 0010 0101 0001 0110 0000 0101

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