Unsigned: Integer ↗ Binary: 1 804 289 383 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 1 804 289 383(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;
  • 1 804 289 383 ÷ 2 = 902 144 691 + 1;
  • 902 144 691 ÷ 2 = 451 072 345 + 1;
  • 451 072 345 ÷ 2 = 225 536 172 + 1;
  • 225 536 172 ÷ 2 = 112 768 086 + 0;
  • 112 768 086 ÷ 2 = 56 384 043 + 0;
  • 56 384 043 ÷ 2 = 28 192 021 + 1;
  • 28 192 021 ÷ 2 = 14 096 010 + 1;
  • 14 096 010 ÷ 2 = 7 048 005 + 0;
  • 7 048 005 ÷ 2 = 3 524 002 + 1;
  • 3 524 002 ÷ 2 = 1 762 001 + 0;
  • 1 762 001 ÷ 2 = 881 000 + 1;
  • 881 000 ÷ 2 = 440 500 + 0;
  • 440 500 ÷ 2 = 220 250 + 0;
  • 220 250 ÷ 2 = 110 125 + 0;
  • 110 125 ÷ 2 = 55 062 + 1;
  • 55 062 ÷ 2 = 27 531 + 0;
  • 27 531 ÷ 2 = 13 765 + 1;
  • 13 765 ÷ 2 = 6 882 + 1;
  • 6 882 ÷ 2 = 3 441 + 0;
  • 3 441 ÷ 2 = 1 720 + 1;
  • 1 720 ÷ 2 = 860 + 0;
  • 860 ÷ 2 = 430 + 0;
  • 430 ÷ 2 = 215 + 0;
  • 215 ÷ 2 = 107 + 1;
  • 107 ÷ 2 = 53 + 1;
  • 53 ÷ 2 = 26 + 1;
  • 26 ÷ 2 = 13 + 0;
  • 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 number:

Take all the remainders starting from the bottom of the list constructed above.


Number 1 804 289 383(10), a positive integer number (with no sign),
converted from decimal system (from base 10)
and written as an unsigned binary (in base 2):

1 804 289 383(10) = 110 1011 1000 1011 0100 0101 0110 0111(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)