Base Two: Unsigned Base Ten Number 27 022 047 Converted To Base Two Binary Code. The Natural Number (Positive Integer, No Sign) Converted From Decimal System and Written As Binary Code

Base ten unsigned number 27 022 047(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;
  • 27 022 047 ÷ 2 = 13 511 023 + 1;
  • 13 511 023 ÷ 2 = 6 755 511 + 1;
  • 6 755 511 ÷ 2 = 3 377 755 + 1;
  • 3 377 755 ÷ 2 = 1 688 877 + 1;
  • 1 688 877 ÷ 2 = 844 438 + 1;
  • 844 438 ÷ 2 = 422 219 + 0;
  • 422 219 ÷ 2 = 211 109 + 1;
  • 211 109 ÷ 2 = 105 554 + 1;
  • 105 554 ÷ 2 = 52 777 + 0;
  • 52 777 ÷ 2 = 26 388 + 1;
  • 26 388 ÷ 2 = 13 194 + 0;
  • 13 194 ÷ 2 = 6 597 + 0;
  • 6 597 ÷ 2 = 3 298 + 1;
  • 3 298 ÷ 2 = 1 649 + 0;
  • 1 649 ÷ 2 = 824 + 1;
  • 824 ÷ 2 = 412 + 0;
  • 412 ÷ 2 = 206 + 0;
  • 206 ÷ 2 = 103 + 0;
  • 103 ÷ 2 = 51 + 1;
  • 51 ÷ 2 = 25 + 1;
  • 25 ÷ 2 = 12 + 1;
  • 12 ÷ 2 = 6 + 0;
  • 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 27 022 047(10), a positive integer number (with no sign),
converted from decimal system (from base 10)
and written as an unsigned binary (in base 2):

27 022 047(10) = 1 1001 1100 0101 0010 1101 1111(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)