Convert 1 637 901 731 551 to a Signed Binary (Base 2)

How to convert 1 637 901 731 551(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 1 637 901 731 551 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;
  • 1 637 901 731 551 ÷ 2 = 818 950 865 775 + 1;
  • 818 950 865 775 ÷ 2 = 409 475 432 887 + 1;
  • 409 475 432 887 ÷ 2 = 204 737 716 443 + 1;
  • 204 737 716 443 ÷ 2 = 102 368 858 221 + 1;
  • 102 368 858 221 ÷ 2 = 51 184 429 110 + 1;
  • 51 184 429 110 ÷ 2 = 25 592 214 555 + 0;
  • 25 592 214 555 ÷ 2 = 12 796 107 277 + 1;
  • 12 796 107 277 ÷ 2 = 6 398 053 638 + 1;
  • 6 398 053 638 ÷ 2 = 3 199 026 819 + 0;
  • 3 199 026 819 ÷ 2 = 1 599 513 409 + 1;
  • 1 599 513 409 ÷ 2 = 799 756 704 + 1;
  • 799 756 704 ÷ 2 = 399 878 352 + 0;
  • 399 878 352 ÷ 2 = 199 939 176 + 0;
  • 199 939 176 ÷ 2 = 99 969 588 + 0;
  • 99 969 588 ÷ 2 = 49 984 794 + 0;
  • 49 984 794 ÷ 2 = 24 992 397 + 0;
  • 24 992 397 ÷ 2 = 12 496 198 + 1;
  • 12 496 198 ÷ 2 = 6 248 099 + 0;
  • 6 248 099 ÷ 2 = 3 124 049 + 1;
  • 3 124 049 ÷ 2 = 1 562 024 + 1;
  • 1 562 024 ÷ 2 = 781 012 + 0;
  • 781 012 ÷ 2 = 390 506 + 0;
  • 390 506 ÷ 2 = 195 253 + 0;
  • 195 253 ÷ 2 = 97 626 + 1;
  • 97 626 ÷ 2 = 48 813 + 0;
  • 48 813 ÷ 2 = 24 406 + 1;
  • 24 406 ÷ 2 = 12 203 + 0;
  • 12 203 ÷ 2 = 6 101 + 1;
  • 6 101 ÷ 2 = 3 050 + 1;
  • 3 050 ÷ 2 = 1 525 + 0;
  • 1 525 ÷ 2 = 762 + 1;
  • 762 ÷ 2 = 381 + 0;
  • 381 ÷ 2 = 190 + 1;
  • 190 ÷ 2 = 95 + 0;
  • 95 ÷ 2 = 47 + 1;
  • 47 ÷ 2 = 23 + 1;
  • 23 ÷ 2 = 11 + 1;
  • 11 ÷ 2 = 5 + 1;
  • 5 ÷ 2 = 2 + 1;
  • 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.

1 637 901 731 551(10) = 1 0111 1101 0101 1010 1000 1101 0000 0110 1101 1111(2)


3. Determine the signed binary number bit length:

  • The base 2 number's actual length, in bits: 41.

  • 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, 41,

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:


1 637 901 731 551(10) Base 10 integer number converted and written as a signed binary code (in base 2):

1 637 901 731 551(10) = 0000 0000 0000 0000 0000 0001 0111 1101 0101 1010 1000 1101 0000 0110 1101 1111

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

Share

» More ops: Convert 1 637 901 731 586, a signed base 10 integer number, write it as a signed binary code (in base 2) equivalent

» Calculations Performed by Our Visitors: Signed base 10 integer numbers converted and written as signed binary code (base 2) equivalents. Data organized on a Monthly Basis

» Month 11, 2025 [November]: Signed base 10 integer numbers converted and written as signed binary code. Calculations performed during the month of: November - by our visitors

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