Unsigned: Integer ↗ Binary: 11 011 011 076 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 11 011 011 076(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;
  • 11 011 011 076 ÷ 2 = 5 505 505 538 + 0;
  • 5 505 505 538 ÷ 2 = 2 752 752 769 + 0;
  • 2 752 752 769 ÷ 2 = 1 376 376 384 + 1;
  • 1 376 376 384 ÷ 2 = 688 188 192 + 0;
  • 688 188 192 ÷ 2 = 344 094 096 + 0;
  • 344 094 096 ÷ 2 = 172 047 048 + 0;
  • 172 047 048 ÷ 2 = 86 023 524 + 0;
  • 86 023 524 ÷ 2 = 43 011 762 + 0;
  • 43 011 762 ÷ 2 = 21 505 881 + 0;
  • 21 505 881 ÷ 2 = 10 752 940 + 1;
  • 10 752 940 ÷ 2 = 5 376 470 + 0;
  • 5 376 470 ÷ 2 = 2 688 235 + 0;
  • 2 688 235 ÷ 2 = 1 344 117 + 1;
  • 1 344 117 ÷ 2 = 672 058 + 1;
  • 672 058 ÷ 2 = 336 029 + 0;
  • 336 029 ÷ 2 = 168 014 + 1;
  • 168 014 ÷ 2 = 84 007 + 0;
  • 84 007 ÷ 2 = 42 003 + 1;
  • 42 003 ÷ 2 = 21 001 + 1;
  • 21 001 ÷ 2 = 10 500 + 1;
  • 10 500 ÷ 2 = 5 250 + 0;
  • 5 250 ÷ 2 = 2 625 + 0;
  • 2 625 ÷ 2 = 1 312 + 1;
  • 1 312 ÷ 2 = 656 + 0;
  • 656 ÷ 2 = 328 + 0;
  • 328 ÷ 2 = 164 + 0;
  • 164 ÷ 2 = 82 + 0;
  • 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 11 011 011 076(10), a positive integer number (with no sign),
converted from decimal system (from base 10)
and written as an unsigned binary (in base 2):

11 011 011 076(10) = 10 1001 0000 0100 1110 1011 0010 0000 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 11 011 011 075 converted from decimal system (from base 10) and written as an unsigned binary (in base 2) = ?

» Unsigned (positive) integer number 11 011 011 077 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)