Signed: Integer ↗ Binary: 31 673 138 067 771 597 Convert the Integer Number to a Signed Binary. Converting and Writing the Base Ten Decimal System Signed Integer as Binary Code (Written in Base Two)

Signed integer number 31 673 138 067 771 597(10)
converted and written as a signed binary (base 2) = ?

1. Divide the number repeatedly by 2:

Keep track of each remainder.

We stop when we get a quotient that is equal to zero.


  • division = quotient + remainder;
  • 31 673 138 067 771 597 ÷ 2 = 15 836 569 033 885 798 + 1;
  • 15 836 569 033 885 798 ÷ 2 = 7 918 284 516 942 899 + 0;
  • 7 918 284 516 942 899 ÷ 2 = 3 959 142 258 471 449 + 1;
  • 3 959 142 258 471 449 ÷ 2 = 1 979 571 129 235 724 + 1;
  • 1 979 571 129 235 724 ÷ 2 = 989 785 564 617 862 + 0;
  • 989 785 564 617 862 ÷ 2 = 494 892 782 308 931 + 0;
  • 494 892 782 308 931 ÷ 2 = 247 446 391 154 465 + 1;
  • 247 446 391 154 465 ÷ 2 = 123 723 195 577 232 + 1;
  • 123 723 195 577 232 ÷ 2 = 61 861 597 788 616 + 0;
  • 61 861 597 788 616 ÷ 2 = 30 930 798 894 308 + 0;
  • 30 930 798 894 308 ÷ 2 = 15 465 399 447 154 + 0;
  • 15 465 399 447 154 ÷ 2 = 7 732 699 723 577 + 0;
  • 7 732 699 723 577 ÷ 2 = 3 866 349 861 788 + 1;
  • 3 866 349 861 788 ÷ 2 = 1 933 174 930 894 + 0;
  • 1 933 174 930 894 ÷ 2 = 966 587 465 447 + 0;
  • 966 587 465 447 ÷ 2 = 483 293 732 723 + 1;
  • 483 293 732 723 ÷ 2 = 241 646 866 361 + 1;
  • 241 646 866 361 ÷ 2 = 120 823 433 180 + 1;
  • 120 823 433 180 ÷ 2 = 60 411 716 590 + 0;
  • 60 411 716 590 ÷ 2 = 30 205 858 295 + 0;
  • 30 205 858 295 ÷ 2 = 15 102 929 147 + 1;
  • 15 102 929 147 ÷ 2 = 7 551 464 573 + 1;
  • 7 551 464 573 ÷ 2 = 3 775 732 286 + 1;
  • 3 775 732 286 ÷ 2 = 1 887 866 143 + 0;
  • 1 887 866 143 ÷ 2 = 943 933 071 + 1;
  • 943 933 071 ÷ 2 = 471 966 535 + 1;
  • 471 966 535 ÷ 2 = 235 983 267 + 1;
  • 235 983 267 ÷ 2 = 117 991 633 + 1;
  • 117 991 633 ÷ 2 = 58 995 816 + 1;
  • 58 995 816 ÷ 2 = 29 497 908 + 0;
  • 29 497 908 ÷ 2 = 14 748 954 + 0;
  • 14 748 954 ÷ 2 = 7 374 477 + 0;
  • 7 374 477 ÷ 2 = 3 687 238 + 1;
  • 3 687 238 ÷ 2 = 1 843 619 + 0;
  • 1 843 619 ÷ 2 = 921 809 + 1;
  • 921 809 ÷ 2 = 460 904 + 1;
  • 460 904 ÷ 2 = 230 452 + 0;
  • 230 452 ÷ 2 = 115 226 + 0;
  • 115 226 ÷ 2 = 57 613 + 0;
  • 57 613 ÷ 2 = 28 806 + 1;
  • 28 806 ÷ 2 = 14 403 + 0;
  • 14 403 ÷ 2 = 7 201 + 1;
  • 7 201 ÷ 2 = 3 600 + 1;
  • 3 600 ÷ 2 = 1 800 + 0;
  • 1 800 ÷ 2 = 900 + 0;
  • 900 ÷ 2 = 450 + 0;
  • 450 ÷ 2 = 225 + 0;
  • 225 ÷ 2 = 112 + 1;
  • 112 ÷ 2 = 56 + 0;
  • 56 ÷ 2 = 28 + 0;
  • 28 ÷ 2 = 14 + 0;
  • 14 ÷ 2 = 7 + 0;
  • 7 ÷ 2 = 3 + 1;
  • 3 ÷ 2 = 1 + 1;
  • 1 ÷ 2 = 0 + 1;

2. Construct the base 2 representation of the positive number:

Take all the remainders starting from the bottom of the list constructed above.


31 673 138 067 771 597(10) = 111 0000 1000 0110 1000 1101 0001 1111 0111 0011 1001 0000 1100 1101(2)


3. Determine the signed binary number bit length:

The base 2 number's actual length, in bits: 55.

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, 55,

3) so that the first bit (leftmost) could be zero
(we deal with a positive number at this moment)

=== is: 64.


4. 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:


Number 31 673 138 067 771 597(10), a signed integer number (with sign),
converted from decimal system (from base 10)
and written as a signed binary (in base 2):

31 673 138 067 771 597(10) = 0000 0000 0111 0000 1000 0110 1000 1101 0001 1111 0111 0011 1001 0000 1100 1101

Spaces were used to group digits: for binary, by 4, for decimal, by 3.

More operations on signed integer numbers:

» Signed integer number 31 673 138 067 771 596 converted from decimal system (from base 10) and written as a signed binary (in base 2) = ?

» Signed integer number 31 673 138 067 771 598 converted from decimal system (from base 10) and written as a signed binary (in base 2) = ?

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How to convert signed integers from decimal system 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