Base Ten to Base Two: Unsigned Number 139 489 489 333 Converted and Written in Base Two. Natural Number (Positive Integer, No Sign) Converted From Decimal System to Binary Code

Base ten unsigned number 139 489 489 333(10) converted and written as a base two binary code

1. Divide the number repeatedly by 2:

Keep track of each remainder.

Stop when getting a quotient that is equal to zero.


  • division = quotient + remainder;
  • 139 489 489 333 ÷ 2 = 69 744 744 666 + 1;
  • 69 744 744 666 ÷ 2 = 34 872 372 333 + 0;
  • 34 872 372 333 ÷ 2 = 17 436 186 166 + 1;
  • 17 436 186 166 ÷ 2 = 8 718 093 083 + 0;
  • 8 718 093 083 ÷ 2 = 4 359 046 541 + 1;
  • 4 359 046 541 ÷ 2 = 2 179 523 270 + 1;
  • 2 179 523 270 ÷ 2 = 1 089 761 635 + 0;
  • 1 089 761 635 ÷ 2 = 544 880 817 + 1;
  • 544 880 817 ÷ 2 = 272 440 408 + 1;
  • 272 440 408 ÷ 2 = 136 220 204 + 0;
  • 136 220 204 ÷ 2 = 68 110 102 + 0;
  • 68 110 102 ÷ 2 = 34 055 051 + 0;
  • 34 055 051 ÷ 2 = 17 027 525 + 1;
  • 17 027 525 ÷ 2 = 8 513 762 + 1;
  • 8 513 762 ÷ 2 = 4 256 881 + 0;
  • 4 256 881 ÷ 2 = 2 128 440 + 1;
  • 2 128 440 ÷ 2 = 1 064 220 + 0;
  • 1 064 220 ÷ 2 = 532 110 + 0;
  • 532 110 ÷ 2 = 266 055 + 0;
  • 266 055 ÷ 2 = 133 027 + 1;
  • 133 027 ÷ 2 = 66 513 + 1;
  • 66 513 ÷ 2 = 33 256 + 1;
  • 33 256 ÷ 2 = 16 628 + 0;
  • 16 628 ÷ 2 = 8 314 + 0;
  • 8 314 ÷ 2 = 4 157 + 0;
  • 4 157 ÷ 2 = 2 078 + 1;
  • 2 078 ÷ 2 = 1 039 + 0;
  • 1 039 ÷ 2 = 519 + 1;
  • 519 ÷ 2 = 259 + 1;
  • 259 ÷ 2 = 129 + 1;
  • 129 ÷ 2 = 64 + 1;
  • 64 ÷ 2 = 32 + 0;
  • 32 ÷ 2 = 16 + 0;
  • 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 139 489 489 333(10), a positive integer number (with no sign),
converted from decimal system (from base 10)
and written as an unsigned binary (in base 2):

139 489 489 333(10) = 10 0000 0111 1010 0011 1000 1011 0001 1011 0101(2)

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

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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)