Unsigned: Integer ↗ Binary: 8 900 313 018 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 8 900 313 018(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;
  • 8 900 313 018 ÷ 2 = 4 450 156 509 + 0;
  • 4 450 156 509 ÷ 2 = 2 225 078 254 + 1;
  • 2 225 078 254 ÷ 2 = 1 112 539 127 + 0;
  • 1 112 539 127 ÷ 2 = 556 269 563 + 1;
  • 556 269 563 ÷ 2 = 278 134 781 + 1;
  • 278 134 781 ÷ 2 = 139 067 390 + 1;
  • 139 067 390 ÷ 2 = 69 533 695 + 0;
  • 69 533 695 ÷ 2 = 34 766 847 + 1;
  • 34 766 847 ÷ 2 = 17 383 423 + 1;
  • 17 383 423 ÷ 2 = 8 691 711 + 1;
  • 8 691 711 ÷ 2 = 4 345 855 + 1;
  • 4 345 855 ÷ 2 = 2 172 927 + 1;
  • 2 172 927 ÷ 2 = 1 086 463 + 1;
  • 1 086 463 ÷ 2 = 543 231 + 1;
  • 543 231 ÷ 2 = 271 615 + 1;
  • 271 615 ÷ 2 = 135 807 + 1;
  • 135 807 ÷ 2 = 67 903 + 1;
  • 67 903 ÷ 2 = 33 951 + 1;
  • 33 951 ÷ 2 = 16 975 + 1;
  • 16 975 ÷ 2 = 8 487 + 1;
  • 8 487 ÷ 2 = 4 243 + 1;
  • 4 243 ÷ 2 = 2 121 + 1;
  • 2 121 ÷ 2 = 1 060 + 1;
  • 1 060 ÷ 2 = 530 + 0;
  • 530 ÷ 2 = 265 + 0;
  • 265 ÷ 2 = 132 + 1;
  • 132 ÷ 2 = 66 + 0;
  • 66 ÷ 2 = 33 + 0;
  • 33 ÷ 2 = 16 + 1;
  • 16 ÷ 2 = 8 + 0;
  • 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.


Number 8 900 313 018(10), a positive integer number (with no sign),
converted from decimal system (from base 10)
and written as an unsigned binary (in base 2):

8 900 313 018(10) = 10 0001 0010 0111 1111 1111 1111 1011 1010(2)

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

More operations on unsigned integer numbers:

» Unsigned (positive) integer number 8 900 313 017 converted from decimal system (from base 10) and written as an unsigned binary (in base 2) = ?

» Unsigned (positive) integer number 8 900 313 019 converted from decimal system (from base 10) and written as an unsigned binary (in base 2) = ?

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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)