Unsigned: Integer ↗ Binary: 111 011 109 998 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 111 011 109 998(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;
  • 111 011 109 998 ÷ 2 = 55 505 554 999 + 0;
  • 55 505 554 999 ÷ 2 = 27 752 777 499 + 1;
  • 27 752 777 499 ÷ 2 = 13 876 388 749 + 1;
  • 13 876 388 749 ÷ 2 = 6 938 194 374 + 1;
  • 6 938 194 374 ÷ 2 = 3 469 097 187 + 0;
  • 3 469 097 187 ÷ 2 = 1 734 548 593 + 1;
  • 1 734 548 593 ÷ 2 = 867 274 296 + 1;
  • 867 274 296 ÷ 2 = 433 637 148 + 0;
  • 433 637 148 ÷ 2 = 216 818 574 + 0;
  • 216 818 574 ÷ 2 = 108 409 287 + 0;
  • 108 409 287 ÷ 2 = 54 204 643 + 1;
  • 54 204 643 ÷ 2 = 27 102 321 + 1;
  • 27 102 321 ÷ 2 = 13 551 160 + 1;
  • 13 551 160 ÷ 2 = 6 775 580 + 0;
  • 6 775 580 ÷ 2 = 3 387 790 + 0;
  • 3 387 790 ÷ 2 = 1 693 895 + 0;
  • 1 693 895 ÷ 2 = 846 947 + 1;
  • 846 947 ÷ 2 = 423 473 + 1;
  • 423 473 ÷ 2 = 211 736 + 1;
  • 211 736 ÷ 2 = 105 868 + 0;
  • 105 868 ÷ 2 = 52 934 + 0;
  • 52 934 ÷ 2 = 26 467 + 0;
  • 26 467 ÷ 2 = 13 233 + 1;
  • 13 233 ÷ 2 = 6 616 + 1;
  • 6 616 ÷ 2 = 3 308 + 0;
  • 3 308 ÷ 2 = 1 654 + 0;
  • 1 654 ÷ 2 = 827 + 0;
  • 827 ÷ 2 = 413 + 1;
  • 413 ÷ 2 = 206 + 1;
  • 206 ÷ 2 = 103 + 0;
  • 103 ÷ 2 = 51 + 1;
  • 51 ÷ 2 = 25 + 1;
  • 25 ÷ 2 = 12 + 1;
  • 12 ÷ 2 = 6 + 0;
  • 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 111 011 109 998(10), a positive integer number (with no sign),
converted from decimal system (from base 10)
and written as an unsigned binary (in base 2):

111 011 109 998(10) = 1 1001 1101 1000 1100 0111 0001 1100 0110 1110(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)