Unsigned: Integer ↗ Binary: 11 111 010 020 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 11 111 010 020(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;
  • 11 111 010 020 ÷ 2 = 5 555 505 010 + 0;
  • 5 555 505 010 ÷ 2 = 2 777 752 505 + 0;
  • 2 777 752 505 ÷ 2 = 1 388 876 252 + 1;
  • 1 388 876 252 ÷ 2 = 694 438 126 + 0;
  • 694 438 126 ÷ 2 = 347 219 063 + 0;
  • 347 219 063 ÷ 2 = 173 609 531 + 1;
  • 173 609 531 ÷ 2 = 86 804 765 + 1;
  • 86 804 765 ÷ 2 = 43 402 382 + 1;
  • 43 402 382 ÷ 2 = 21 701 191 + 0;
  • 21 701 191 ÷ 2 = 10 850 595 + 1;
  • 10 850 595 ÷ 2 = 5 425 297 + 1;
  • 5 425 297 ÷ 2 = 2 712 648 + 1;
  • 2 712 648 ÷ 2 = 1 356 324 + 0;
  • 1 356 324 ÷ 2 = 678 162 + 0;
  • 678 162 ÷ 2 = 339 081 + 0;
  • 339 081 ÷ 2 = 169 540 + 1;
  • 169 540 ÷ 2 = 84 770 + 0;
  • 84 770 ÷ 2 = 42 385 + 0;
  • 42 385 ÷ 2 = 21 192 + 1;
  • 21 192 ÷ 2 = 10 596 + 0;
  • 10 596 ÷ 2 = 5 298 + 0;
  • 5 298 ÷ 2 = 2 649 + 0;
  • 2 649 ÷ 2 = 1 324 + 1;
  • 1 324 ÷ 2 = 662 + 0;
  • 662 ÷ 2 = 331 + 0;
  • 331 ÷ 2 = 165 + 1;
  • 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 11 111 010 020(10), a positive integer number (with no sign),
converted from decimal system (from base 10)
and written as an unsigned binary (in base 2):

11 111 010 020(10) = 10 1001 0110 0100 0100 1000 1110 1110 0100(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 11 111 010 019 converted from decimal system (from base 10) and written as an unsigned binary (in base 2) = ?

» Unsigned (positive) integer number 11 111 010 021 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)