Base Ten to Base Two: Unsigned Number 24 091 999 Converted and Written in Base Two. Natural Number (Positive Integer, No Sign) Converted From Decimal System to Binary Code

Base ten unsigned number 24 091 999(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;
  • 24 091 999 ÷ 2 = 12 045 999 + 1;
  • 12 045 999 ÷ 2 = 6 022 999 + 1;
  • 6 022 999 ÷ 2 = 3 011 499 + 1;
  • 3 011 499 ÷ 2 = 1 505 749 + 1;
  • 1 505 749 ÷ 2 = 752 874 + 1;
  • 752 874 ÷ 2 = 376 437 + 0;
  • 376 437 ÷ 2 = 188 218 + 1;
  • 188 218 ÷ 2 = 94 109 + 0;
  • 94 109 ÷ 2 = 47 054 + 1;
  • 47 054 ÷ 2 = 23 527 + 0;
  • 23 527 ÷ 2 = 11 763 + 1;
  • 11 763 ÷ 2 = 5 881 + 1;
  • 5 881 ÷ 2 = 2 940 + 1;
  • 2 940 ÷ 2 = 1 470 + 0;
  • 1 470 ÷ 2 = 735 + 0;
  • 735 ÷ 2 = 367 + 1;
  • 367 ÷ 2 = 183 + 1;
  • 183 ÷ 2 = 91 + 1;
  • 91 ÷ 2 = 45 + 1;
  • 45 ÷ 2 = 22 + 1;
  • 22 ÷ 2 = 11 + 0;
  • 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.


Number 24 091 999(10), a positive integer number (with no sign),
converted from decimal system (from base 10)
and written as an unsigned binary (in base 2):

24 091 999(10) = 1 0110 1111 1001 1101 0101 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)