Unsigned: Integer ↗ Binary: 3 698 745 123 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 3 698 745 123(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;
  • 3 698 745 123 ÷ 2 = 1 849 372 561 + 1;
  • 1 849 372 561 ÷ 2 = 924 686 280 + 1;
  • 924 686 280 ÷ 2 = 462 343 140 + 0;
  • 462 343 140 ÷ 2 = 231 171 570 + 0;
  • 231 171 570 ÷ 2 = 115 585 785 + 0;
  • 115 585 785 ÷ 2 = 57 792 892 + 1;
  • 57 792 892 ÷ 2 = 28 896 446 + 0;
  • 28 896 446 ÷ 2 = 14 448 223 + 0;
  • 14 448 223 ÷ 2 = 7 224 111 + 1;
  • 7 224 111 ÷ 2 = 3 612 055 + 1;
  • 3 612 055 ÷ 2 = 1 806 027 + 1;
  • 1 806 027 ÷ 2 = 903 013 + 1;
  • 903 013 ÷ 2 = 451 506 + 1;
  • 451 506 ÷ 2 = 225 753 + 0;
  • 225 753 ÷ 2 = 112 876 + 1;
  • 112 876 ÷ 2 = 56 438 + 0;
  • 56 438 ÷ 2 = 28 219 + 0;
  • 28 219 ÷ 2 = 14 109 + 1;
  • 14 109 ÷ 2 = 7 054 + 1;
  • 7 054 ÷ 2 = 3 527 + 0;
  • 3 527 ÷ 2 = 1 763 + 1;
  • 1 763 ÷ 2 = 881 + 1;
  • 881 ÷ 2 = 440 + 1;
  • 440 ÷ 2 = 220 + 0;
  • 220 ÷ 2 = 110 + 0;
  • 110 ÷ 2 = 55 + 0;
  • 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 number:

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


Number 3 698 745 123(10), a positive integer number (with no sign),
converted from decimal system (from base 10)
and written as an unsigned binary (in base 2):

3 698 745 123(10) = 1101 1100 0111 0110 0101 1111 0010 0011(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 3 698 745 122 converted from decimal system (from base 10) and written as an unsigned binary (in base 2) = ?

» Unsigned (positive) integer number 3 698 745 124 converted from decimal system (from base 10) and written as an unsigned binary (in base 2) = ?

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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)