Convert 587 447 587 063 to a Signed Binary (Base 2)

How to convert 587 447 587 063(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 587 447 587 063 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. 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;
  • 587 447 587 063 ÷ 2 = 293 723 793 531 + 1;
  • 293 723 793 531 ÷ 2 = 146 861 896 765 + 1;
  • 146 861 896 765 ÷ 2 = 73 430 948 382 + 1;
  • 73 430 948 382 ÷ 2 = 36 715 474 191 + 0;
  • 36 715 474 191 ÷ 2 = 18 357 737 095 + 1;
  • 18 357 737 095 ÷ 2 = 9 178 868 547 + 1;
  • 9 178 868 547 ÷ 2 = 4 589 434 273 + 1;
  • 4 589 434 273 ÷ 2 = 2 294 717 136 + 1;
  • 2 294 717 136 ÷ 2 = 1 147 358 568 + 0;
  • 1 147 358 568 ÷ 2 = 573 679 284 + 0;
  • 573 679 284 ÷ 2 = 286 839 642 + 0;
  • 286 839 642 ÷ 2 = 143 419 821 + 0;
  • 143 419 821 ÷ 2 = 71 709 910 + 1;
  • 71 709 910 ÷ 2 = 35 854 955 + 0;
  • 35 854 955 ÷ 2 = 17 927 477 + 1;
  • 17 927 477 ÷ 2 = 8 963 738 + 1;
  • 8 963 738 ÷ 2 = 4 481 869 + 0;
  • 4 481 869 ÷ 2 = 2 240 934 + 1;
  • 2 240 934 ÷ 2 = 1 120 467 + 0;
  • 1 120 467 ÷ 2 = 560 233 + 1;
  • 560 233 ÷ 2 = 280 116 + 1;
  • 280 116 ÷ 2 = 140 058 + 0;
  • 140 058 ÷ 2 = 70 029 + 0;
  • 70 029 ÷ 2 = 35 014 + 1;
  • 35 014 ÷ 2 = 17 507 + 0;
  • 17 507 ÷ 2 = 8 753 + 1;
  • 8 753 ÷ 2 = 4 376 + 1;
  • 4 376 ÷ 2 = 2 188 + 0;
  • 2 188 ÷ 2 = 1 094 + 0;
  • 1 094 ÷ 2 = 547 + 0;
  • 547 ÷ 2 = 273 + 1;
  • 273 ÷ 2 = 136 + 1;
  • 136 ÷ 2 = 68 + 0;
  • 68 ÷ 2 = 34 + 0;
  • 34 ÷ 2 = 17 + 0;
  • 17 ÷ 2 = 8 + 1;
  • 8 ÷ 2 = 4 + 0;
  • 4 ÷ 2 = 2 + 0;
  • 2 ÷ 2 = 1 + 0;
  • 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.

587 447 587 063(10) = 1000 1000 1100 0110 1001 1010 1101 0000 1111 0111(2)


3. Determine the signed binary number bit length:

  • The base 2 number's actual length, in bits: 40.

  • 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, 40,

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:


587 447 587 063(10) Base 10 integer number converted and written as a signed binary code (in base 2):

587 447 587 063(10) = 0000 0000 0000 0000 0000 0000 1000 1000 1100 0110 1001 1010 1101 0000 1111 0111

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