Unsigned: Integer ↗ Binary: 11 101 110 111 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 11 101 110 111(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;
  • 11 101 110 111 ÷ 2 = 5 550 555 055 + 1;
  • 5 550 555 055 ÷ 2 = 2 775 277 527 + 1;
  • 2 775 277 527 ÷ 2 = 1 387 638 763 + 1;
  • 1 387 638 763 ÷ 2 = 693 819 381 + 1;
  • 693 819 381 ÷ 2 = 346 909 690 + 1;
  • 346 909 690 ÷ 2 = 173 454 845 + 0;
  • 173 454 845 ÷ 2 = 86 727 422 + 1;
  • 86 727 422 ÷ 2 = 43 363 711 + 0;
  • 43 363 711 ÷ 2 = 21 681 855 + 1;
  • 21 681 855 ÷ 2 = 10 840 927 + 1;
  • 10 840 927 ÷ 2 = 5 420 463 + 1;
  • 5 420 463 ÷ 2 = 2 710 231 + 1;
  • 2 710 231 ÷ 2 = 1 355 115 + 1;
  • 1 355 115 ÷ 2 = 677 557 + 1;
  • 677 557 ÷ 2 = 338 778 + 1;
  • 338 778 ÷ 2 = 169 389 + 0;
  • 169 389 ÷ 2 = 84 694 + 1;
  • 84 694 ÷ 2 = 42 347 + 0;
  • 42 347 ÷ 2 = 21 173 + 1;
  • 21 173 ÷ 2 = 10 586 + 1;
  • 10 586 ÷ 2 = 5 293 + 0;
  • 5 293 ÷ 2 = 2 646 + 1;
  • 2 646 ÷ 2 = 1 323 + 0;
  • 1 323 ÷ 2 = 661 + 1;
  • 661 ÷ 2 = 330 + 1;
  • 330 ÷ 2 = 165 + 0;
  • 165 ÷ 2 = 82 + 1;
  • 82 ÷ 2 = 41 + 0;
  • 41 ÷ 2 = 20 + 1;
  • 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 11 101 110 111(10), a positive integer number (with no sign),
converted from decimal system (from base 10)
and written as an unsigned binary (in base 2):

11 101 110 111(10) = 10 1001 0101 1010 1101 0111 1111 0101 1111(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 11 101 110 110 converted from decimal system (from base 10) and written as an unsigned binary (in base 2) = ?

» Unsigned (positive) integer number 11 101 110 112 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)