Convert -731 199 020 484 759 508 to a Signed Binary (Base 2)

How to convert -731 199 020 484 759 508(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 -731 199 020 484 759 508 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:

|-731 199 020 484 759 508| = 731 199 020 484 759 508

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;
  • 731 199 020 484 759 508 ÷ 2 = 365 599 510 242 379 754 + 0;
  • 365 599 510 242 379 754 ÷ 2 = 182 799 755 121 189 877 + 0;
  • 182 799 755 121 189 877 ÷ 2 = 91 399 877 560 594 938 + 1;
  • 91 399 877 560 594 938 ÷ 2 = 45 699 938 780 297 469 + 0;
  • 45 699 938 780 297 469 ÷ 2 = 22 849 969 390 148 734 + 1;
  • 22 849 969 390 148 734 ÷ 2 = 11 424 984 695 074 367 + 0;
  • 11 424 984 695 074 367 ÷ 2 = 5 712 492 347 537 183 + 1;
  • 5 712 492 347 537 183 ÷ 2 = 2 856 246 173 768 591 + 1;
  • 2 856 246 173 768 591 ÷ 2 = 1 428 123 086 884 295 + 1;
  • 1 428 123 086 884 295 ÷ 2 = 714 061 543 442 147 + 1;
  • 714 061 543 442 147 ÷ 2 = 357 030 771 721 073 + 1;
  • 357 030 771 721 073 ÷ 2 = 178 515 385 860 536 + 1;
  • 178 515 385 860 536 ÷ 2 = 89 257 692 930 268 + 0;
  • 89 257 692 930 268 ÷ 2 = 44 628 846 465 134 + 0;
  • 44 628 846 465 134 ÷ 2 = 22 314 423 232 567 + 0;
  • 22 314 423 232 567 ÷ 2 = 11 157 211 616 283 + 1;
  • 11 157 211 616 283 ÷ 2 = 5 578 605 808 141 + 1;
  • 5 578 605 808 141 ÷ 2 = 2 789 302 904 070 + 1;
  • 2 789 302 904 070 ÷ 2 = 1 394 651 452 035 + 0;
  • 1 394 651 452 035 ÷ 2 = 697 325 726 017 + 1;
  • 697 325 726 017 ÷ 2 = 348 662 863 008 + 1;
  • 348 662 863 008 ÷ 2 = 174 331 431 504 + 0;
  • 174 331 431 504 ÷ 2 = 87 165 715 752 + 0;
  • 87 165 715 752 ÷ 2 = 43 582 857 876 + 0;
  • 43 582 857 876 ÷ 2 = 21 791 428 938 + 0;
  • 21 791 428 938 ÷ 2 = 10 895 714 469 + 0;
  • 10 895 714 469 ÷ 2 = 5 447 857 234 + 1;
  • 5 447 857 234 ÷ 2 = 2 723 928 617 + 0;
  • 2 723 928 617 ÷ 2 = 1 361 964 308 + 1;
  • 1 361 964 308 ÷ 2 = 680 982 154 + 0;
  • 680 982 154 ÷ 2 = 340 491 077 + 0;
  • 340 491 077 ÷ 2 = 170 245 538 + 1;
  • 170 245 538 ÷ 2 = 85 122 769 + 0;
  • 85 122 769 ÷ 2 = 42 561 384 + 1;
  • 42 561 384 ÷ 2 = 21 280 692 + 0;
  • 21 280 692 ÷ 2 = 10 640 346 + 0;
  • 10 640 346 ÷ 2 = 5 320 173 + 0;
  • 5 320 173 ÷ 2 = 2 660 086 + 1;
  • 2 660 086 ÷ 2 = 1 330 043 + 0;
  • 1 330 043 ÷ 2 = 665 021 + 1;
  • 665 021 ÷ 2 = 332 510 + 1;
  • 332 510 ÷ 2 = 166 255 + 0;
  • 166 255 ÷ 2 = 83 127 + 1;
  • 83 127 ÷ 2 = 41 563 + 1;
  • 41 563 ÷ 2 = 20 781 + 1;
  • 20 781 ÷ 2 = 10 390 + 1;
  • 10 390 ÷ 2 = 5 195 + 0;
  • 5 195 ÷ 2 = 2 597 + 1;
  • 2 597 ÷ 2 = 1 298 + 1;
  • 1 298 ÷ 2 = 649 + 0;
  • 649 ÷ 2 = 324 + 1;
  • 324 ÷ 2 = 162 + 0;
  • 162 ÷ 2 = 81 + 0;
  • 81 ÷ 2 = 40 + 1;
  • 40 ÷ 2 = 20 + 0;
  • 20 ÷ 2 = 10 + 0;
  • 10 ÷ 2 = 5 + 0;
  • 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.

731 199 020 484 759 508(10) = 1010 0010 0101 1011 1101 1010 0010 1001 0100 0001 1011 1000 1111 1101 0100(2)


4. Determine the signed binary number bit length:

  • The base 2 number's actual length, in bits: 60.

  • 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, 60,

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:


731 199 020 484 759 508(10) = 0000 1010 0010 0101 1011 1101 1010 0010 1001 0100 0001 1011 1000 1111 1101 0100

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...


-731 199 020 484 759 508(10) Base 10 integer number converted and written as a signed binary code (in base 2):

-731 199 020 484 759 508(10) = 1000 1010 0010 0101 1011 1101 1010 0010 1001 0100 0001 1011 1000 1111 1101 0100

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