Unsigned: Integer ↗ Binary: 10 101 100 108 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 10 101 100 108(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;
  • 10 101 100 108 ÷ 2 = 5 050 550 054 + 0;
  • 5 050 550 054 ÷ 2 = 2 525 275 027 + 0;
  • 2 525 275 027 ÷ 2 = 1 262 637 513 + 1;
  • 1 262 637 513 ÷ 2 = 631 318 756 + 1;
  • 631 318 756 ÷ 2 = 315 659 378 + 0;
  • 315 659 378 ÷ 2 = 157 829 689 + 0;
  • 157 829 689 ÷ 2 = 78 914 844 + 1;
  • 78 914 844 ÷ 2 = 39 457 422 + 0;
  • 39 457 422 ÷ 2 = 19 728 711 + 0;
  • 19 728 711 ÷ 2 = 9 864 355 + 1;
  • 9 864 355 ÷ 2 = 4 932 177 + 1;
  • 4 932 177 ÷ 2 = 2 466 088 + 1;
  • 2 466 088 ÷ 2 = 1 233 044 + 0;
  • 1 233 044 ÷ 2 = 616 522 + 0;
  • 616 522 ÷ 2 = 308 261 + 0;
  • 308 261 ÷ 2 = 154 130 + 1;
  • 154 130 ÷ 2 = 77 065 + 0;
  • 77 065 ÷ 2 = 38 532 + 1;
  • 38 532 ÷ 2 = 19 266 + 0;
  • 19 266 ÷ 2 = 9 633 + 0;
  • 9 633 ÷ 2 = 4 816 + 1;
  • 4 816 ÷ 2 = 2 408 + 0;
  • 2 408 ÷ 2 = 1 204 + 0;
  • 1 204 ÷ 2 = 602 + 0;
  • 602 ÷ 2 = 301 + 0;
  • 301 ÷ 2 = 150 + 1;
  • 150 ÷ 2 = 75 + 0;
  • 75 ÷ 2 = 37 + 1;
  • 37 ÷ 2 = 18 + 1;
  • 18 ÷ 2 = 9 + 0;
  • 9 ÷ 2 = 4 + 1;
  • 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 10 101 100 108(10), a positive integer number (with no sign),
converted from decimal system (from base 10)
and written as an unsigned binary (in base 2):

10 101 100 108(10) = 10 0101 1010 0001 0010 1000 1110 0100 1100(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 10 101 100 107 converted from decimal system (from base 10) and written as an unsigned binary (in base 2) = ?

» Unsigned (positive) integer number 10 101 100 109 converted from decimal system (from base 10) and written as an unsigned binary (in base 2) = ?

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All the decimal system (written in base ten) positive integers (with no sign) converted to unsigned binary (in base 2)

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)