Unsigned: Integer ↗ Binary: 21 474 883 666 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 21 474 883 666(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;
  • 21 474 883 666 ÷ 2 = 10 737 441 833 + 0;
  • 10 737 441 833 ÷ 2 = 5 368 720 916 + 1;
  • 5 368 720 916 ÷ 2 = 2 684 360 458 + 0;
  • 2 684 360 458 ÷ 2 = 1 342 180 229 + 0;
  • 1 342 180 229 ÷ 2 = 671 090 114 + 1;
  • 671 090 114 ÷ 2 = 335 545 057 + 0;
  • 335 545 057 ÷ 2 = 167 772 528 + 1;
  • 167 772 528 ÷ 2 = 83 886 264 + 0;
  • 83 886 264 ÷ 2 = 41 943 132 + 0;
  • 41 943 132 ÷ 2 = 20 971 566 + 0;
  • 20 971 566 ÷ 2 = 10 485 783 + 0;
  • 10 485 783 ÷ 2 = 5 242 891 + 1;
  • 5 242 891 ÷ 2 = 2 621 445 + 1;
  • 2 621 445 ÷ 2 = 1 310 722 + 1;
  • 1 310 722 ÷ 2 = 655 361 + 0;
  • 655 361 ÷ 2 = 327 680 + 1;
  • 327 680 ÷ 2 = 163 840 + 0;
  • 163 840 ÷ 2 = 81 920 + 0;
  • 81 920 ÷ 2 = 40 960 + 0;
  • 40 960 ÷ 2 = 20 480 + 0;
  • 20 480 ÷ 2 = 10 240 + 0;
  • 10 240 ÷ 2 = 5 120 + 0;
  • 5 120 ÷ 2 = 2 560 + 0;
  • 2 560 ÷ 2 = 1 280 + 0;
  • 1 280 ÷ 2 = 640 + 0;
  • 640 ÷ 2 = 320 + 0;
  • 320 ÷ 2 = 160 + 0;
  • 160 ÷ 2 = 80 + 0;
  • 80 ÷ 2 = 40 + 0;
  • 40 ÷ 2 = 20 + 0;
  • 20 ÷ 2 = 10 + 0;
  • 10 ÷ 2 = 5 + 0;
  • 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 21 474 883 666(10), a positive integer number (with no sign),
converted from decimal system (from base 10)
and written as an unsigned binary (in base 2):

21 474 883 666(10) = 101 0000 0000 0000 0000 1011 1000 0101 0010(2)

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

The latest positive (unsigned) integer numbers converted from decimal system (written in base ten) to unsigned binary (written in base two)

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)