Unsigned: Integer ↗ Binary: 3 627 933 333 Convert the Positive Integer (Whole Number) From Base Ten (10) To Base Two (2), Conversion and Writing of Decimal System Number as Unsigned Binary Code

Unsigned (positive) integer number 3 627 933 333(10)
converted and written as an unsigned binary (base 2) = ?

1. 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;
  • 3 627 933 333 ÷ 2 = 1 813 966 666 + 1;
  • 1 813 966 666 ÷ 2 = 906 983 333 + 0;
  • 906 983 333 ÷ 2 = 453 491 666 + 1;
  • 453 491 666 ÷ 2 = 226 745 833 + 0;
  • 226 745 833 ÷ 2 = 113 372 916 + 1;
  • 113 372 916 ÷ 2 = 56 686 458 + 0;
  • 56 686 458 ÷ 2 = 28 343 229 + 0;
  • 28 343 229 ÷ 2 = 14 171 614 + 1;
  • 14 171 614 ÷ 2 = 7 085 807 + 0;
  • 7 085 807 ÷ 2 = 3 542 903 + 1;
  • 3 542 903 ÷ 2 = 1 771 451 + 1;
  • 1 771 451 ÷ 2 = 885 725 + 1;
  • 885 725 ÷ 2 = 442 862 + 1;
  • 442 862 ÷ 2 = 221 431 + 0;
  • 221 431 ÷ 2 = 110 715 + 1;
  • 110 715 ÷ 2 = 55 357 + 1;
  • 55 357 ÷ 2 = 27 678 + 1;
  • 27 678 ÷ 2 = 13 839 + 0;
  • 13 839 ÷ 2 = 6 919 + 1;
  • 6 919 ÷ 2 = 3 459 + 1;
  • 3 459 ÷ 2 = 1 729 + 1;
  • 1 729 ÷ 2 = 864 + 1;
  • 864 ÷ 2 = 432 + 0;
  • 432 ÷ 2 = 216 + 0;
  • 216 ÷ 2 = 108 + 0;
  • 108 ÷ 2 = 54 + 0;
  • 54 ÷ 2 = 27 + 0;
  • 27 ÷ 2 = 13 + 1;
  • 13 ÷ 2 = 6 + 1;
  • 6 ÷ 2 = 3 + 0;
  • 3 ÷ 2 = 1 + 1;
  • 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.


Number 3 627 933 333(10), a positive integer number (with no sign),
converted from decimal system (from base 10)
and written as an unsigned binary (in base 2):

3 627 933 333(10) = 1101 1000 0011 1101 1101 1110 1001 0101(2)

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

The latest positive (unsigned) integer numbers converted from decimal system (written in base ten) to unsigned binary (written in base two)

How to convert unsigned integer numbers (positive) from decimal system (base 10) to binary = simply convert from base ten to base two

Follow the steps below to convert a base ten unsigned integer number to base two:

  • 1. Divide repeatedly by 2 the positive integer number that has to be converted to binary, keeping track of each remainder, until we get a QUOTIENT that is equal to ZERO.
  • 2. Construct the base 2 representation of the positive integer 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).

Example: convert the positive integer number 55 from decimal system (base ten) to binary code (base two):

  • 1. Divide repeatedly 55 by 2, keeping track of each remainder, until we get a quotient that is equal to zero:
    • division = quotient + remainder;
    • 55 ÷ 2 = 27 + 1;
    • 27 ÷ 2 = 13 + 1;
    • 13 ÷ 2 = 6 + 1;
    • 6 ÷ 2 = 3 + 0;
    • 3 ÷ 2 = 1 + 1;
    • 1 ÷ 2 = 0 + 1;
  • 2. Construct the base 2 representation of the positive integer number, by taking all the remainders starting from the bottom of the list constructed above:
    55(10) = 11 0111(2)
  • Number 5510, positive integer (no sign), converted from decimal system (base 10) to unsigned binary (base 2) = 11 0111(2)