Signed: Integer ↗ Binary: -3 530 914 537 127 759 994 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 -3 530 914 537 127 759 994(10)
converted and written as a signed binary (base 2) = ?

1. Start with the positive version of the number:

|-3 530 914 537 127 759 994| = 3 530 914 537 127 759 994

2. 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;
  • 3 530 914 537 127 759 994 ÷ 2 = 1 765 457 268 563 879 997 + 0;
  • 1 765 457 268 563 879 997 ÷ 2 = 882 728 634 281 939 998 + 1;
  • 882 728 634 281 939 998 ÷ 2 = 441 364 317 140 969 999 + 0;
  • 441 364 317 140 969 999 ÷ 2 = 220 682 158 570 484 999 + 1;
  • 220 682 158 570 484 999 ÷ 2 = 110 341 079 285 242 499 + 1;
  • 110 341 079 285 242 499 ÷ 2 = 55 170 539 642 621 249 + 1;
  • 55 170 539 642 621 249 ÷ 2 = 27 585 269 821 310 624 + 1;
  • 27 585 269 821 310 624 ÷ 2 = 13 792 634 910 655 312 + 0;
  • 13 792 634 910 655 312 ÷ 2 = 6 896 317 455 327 656 + 0;
  • 6 896 317 455 327 656 ÷ 2 = 3 448 158 727 663 828 + 0;
  • 3 448 158 727 663 828 ÷ 2 = 1 724 079 363 831 914 + 0;
  • 1 724 079 363 831 914 ÷ 2 = 862 039 681 915 957 + 0;
  • 862 039 681 915 957 ÷ 2 = 431 019 840 957 978 + 1;
  • 431 019 840 957 978 ÷ 2 = 215 509 920 478 989 + 0;
  • 215 509 920 478 989 ÷ 2 = 107 754 960 239 494 + 1;
  • 107 754 960 239 494 ÷ 2 = 53 877 480 119 747 + 0;
  • 53 877 480 119 747 ÷ 2 = 26 938 740 059 873 + 1;
  • 26 938 740 059 873 ÷ 2 = 13 469 370 029 936 + 1;
  • 13 469 370 029 936 ÷ 2 = 6 734 685 014 968 + 0;
  • 6 734 685 014 968 ÷ 2 = 3 367 342 507 484 + 0;
  • 3 367 342 507 484 ÷ 2 = 1 683 671 253 742 + 0;
  • 1 683 671 253 742 ÷ 2 = 841 835 626 871 + 0;
  • 841 835 626 871 ÷ 2 = 420 917 813 435 + 1;
  • 420 917 813 435 ÷ 2 = 210 458 906 717 + 1;
  • 210 458 906 717 ÷ 2 = 105 229 453 358 + 1;
  • 105 229 453 358 ÷ 2 = 52 614 726 679 + 0;
  • 52 614 726 679 ÷ 2 = 26 307 363 339 + 1;
  • 26 307 363 339 ÷ 2 = 13 153 681 669 + 1;
  • 13 153 681 669 ÷ 2 = 6 576 840 834 + 1;
  • 6 576 840 834 ÷ 2 = 3 288 420 417 + 0;
  • 3 288 420 417 ÷ 2 = 1 644 210 208 + 1;
  • 1 644 210 208 ÷ 2 = 822 105 104 + 0;
  • 822 105 104 ÷ 2 = 411 052 552 + 0;
  • 411 052 552 ÷ 2 = 205 526 276 + 0;
  • 205 526 276 ÷ 2 = 102 763 138 + 0;
  • 102 763 138 ÷ 2 = 51 381 569 + 0;
  • 51 381 569 ÷ 2 = 25 690 784 + 1;
  • 25 690 784 ÷ 2 = 12 845 392 + 0;
  • 12 845 392 ÷ 2 = 6 422 696 + 0;
  • 6 422 696 ÷ 2 = 3 211 348 + 0;
  • 3 211 348 ÷ 2 = 1 605 674 + 0;
  • 1 605 674 ÷ 2 = 802 837 + 0;
  • 802 837 ÷ 2 = 401 418 + 1;
  • 401 418 ÷ 2 = 200 709 + 0;
  • 200 709 ÷ 2 = 100 354 + 1;
  • 100 354 ÷ 2 = 50 177 + 0;
  • 50 177 ÷ 2 = 25 088 + 1;
  • 25 088 ÷ 2 = 12 544 + 0;
  • 12 544 ÷ 2 = 6 272 + 0;
  • 6 272 ÷ 2 = 3 136 + 0;
  • 3 136 ÷ 2 = 1 568 + 0;
  • 1 568 ÷ 2 = 784 + 0;
  • 784 ÷ 2 = 392 + 0;
  • 392 ÷ 2 = 196 + 0;
  • 196 ÷ 2 = 98 + 0;
  • 98 ÷ 2 = 49 + 0;
  • 49 ÷ 2 = 24 + 1;
  • 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.


3 530 914 537 127 759 994(10) = 11 0001 0000 0000 0101 0100 0001 0000 0101 1101 1100 0011 0101 0000 0111 1010(2)


4. Determine the signed binary number bit length:

The base 2 number's actual length, in bits: 62.

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, 62,

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:


3 530 914 537 127 759 994(10) = 0011 0001 0000 0000 0101 0100 0001 0000 0101 1101 1100 0011 0101 0000 0111 1010


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...


Number -3 530 914 537 127 759 994(10), a signed integer number (with sign),
converted from decimal system (from base 10)
and written as a signed binary (in base 2):

-3 530 914 537 127 759 994(10) = 1011 0001 0000 0000 0101 0100 0001 0000 0101 1101 1100 0011 0101 0000 0111 1010

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

More operations on signed integer numbers:

» Signed integer number -3 530 914 537 127 759 995 converted from decimal system (from base 10) and written as a signed binary (in base 2) = ?

» Signed integer number -3 530 914 537 127 759 993 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