Convert -35 482 157 703 228 201 to a Signed Binary (Base 2)

How to convert -35 482 157 703 228 201(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 -35 482 157 703 228 201 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:

|-35 482 157 703 228 201| = 35 482 157 703 228 201

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;
  • 35 482 157 703 228 201 ÷ 2 = 17 741 078 851 614 100 + 1;
  • 17 741 078 851 614 100 ÷ 2 = 8 870 539 425 807 050 + 0;
  • 8 870 539 425 807 050 ÷ 2 = 4 435 269 712 903 525 + 0;
  • 4 435 269 712 903 525 ÷ 2 = 2 217 634 856 451 762 + 1;
  • 2 217 634 856 451 762 ÷ 2 = 1 108 817 428 225 881 + 0;
  • 1 108 817 428 225 881 ÷ 2 = 554 408 714 112 940 + 1;
  • 554 408 714 112 940 ÷ 2 = 277 204 357 056 470 + 0;
  • 277 204 357 056 470 ÷ 2 = 138 602 178 528 235 + 0;
  • 138 602 178 528 235 ÷ 2 = 69 301 089 264 117 + 1;
  • 69 301 089 264 117 ÷ 2 = 34 650 544 632 058 + 1;
  • 34 650 544 632 058 ÷ 2 = 17 325 272 316 029 + 0;
  • 17 325 272 316 029 ÷ 2 = 8 662 636 158 014 + 1;
  • 8 662 636 158 014 ÷ 2 = 4 331 318 079 007 + 0;
  • 4 331 318 079 007 ÷ 2 = 2 165 659 039 503 + 1;
  • 2 165 659 039 503 ÷ 2 = 1 082 829 519 751 + 1;
  • 1 082 829 519 751 ÷ 2 = 541 414 759 875 + 1;
  • 541 414 759 875 ÷ 2 = 270 707 379 937 + 1;
  • 270 707 379 937 ÷ 2 = 135 353 689 968 + 1;
  • 135 353 689 968 ÷ 2 = 67 676 844 984 + 0;
  • 67 676 844 984 ÷ 2 = 33 838 422 492 + 0;
  • 33 838 422 492 ÷ 2 = 16 919 211 246 + 0;
  • 16 919 211 246 ÷ 2 = 8 459 605 623 + 0;
  • 8 459 605 623 ÷ 2 = 4 229 802 811 + 1;
  • 4 229 802 811 ÷ 2 = 2 114 901 405 + 1;
  • 2 114 901 405 ÷ 2 = 1 057 450 702 + 1;
  • 1 057 450 702 ÷ 2 = 528 725 351 + 0;
  • 528 725 351 ÷ 2 = 264 362 675 + 1;
  • 264 362 675 ÷ 2 = 132 181 337 + 1;
  • 132 181 337 ÷ 2 = 66 090 668 + 1;
  • 66 090 668 ÷ 2 = 33 045 334 + 0;
  • 33 045 334 ÷ 2 = 16 522 667 + 0;
  • 16 522 667 ÷ 2 = 8 261 333 + 1;
  • 8 261 333 ÷ 2 = 4 130 666 + 1;
  • 4 130 666 ÷ 2 = 2 065 333 + 0;
  • 2 065 333 ÷ 2 = 1 032 666 + 1;
  • 1 032 666 ÷ 2 = 516 333 + 0;
  • 516 333 ÷ 2 = 258 166 + 1;
  • 258 166 ÷ 2 = 129 083 + 0;
  • 129 083 ÷ 2 = 64 541 + 1;
  • 64 541 ÷ 2 = 32 270 + 1;
  • 32 270 ÷ 2 = 16 135 + 0;
  • 16 135 ÷ 2 = 8 067 + 1;
  • 8 067 ÷ 2 = 4 033 + 1;
  • 4 033 ÷ 2 = 2 016 + 1;
  • 2 016 ÷ 2 = 1 008 + 0;
  • 1 008 ÷ 2 = 504 + 0;
  • 504 ÷ 2 = 252 + 0;
  • 252 ÷ 2 = 126 + 0;
  • 126 ÷ 2 = 63 + 0;
  • 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:

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

35 482 157 703 228 201(10) = 111 1110 0000 1110 1101 0101 1001 1101 1100 0011 1110 1011 0010 1001(2)


4. 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.


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:


35 482 157 703 228 201(10) = 0000 0000 0111 1110 0000 1110 1101 0101 1001 1101 1100 0011 1110 1011 0010 1001

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...


-35 482 157 703 228 201(10) Base 10 integer number converted and written as a signed binary code (in base 2):

-35 482 157 703 228 201(10) = 1000 0000 0111 1110 0000 1110 1101 0101 1001 1101 1100 0011 1110 1011 0010 1001

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