Unsigned: Integer ↗ Binary: 11 000 110 003 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 11 000 110 003(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;
  • 11 000 110 003 ÷ 2 = 5 500 055 001 + 1;
  • 5 500 055 001 ÷ 2 = 2 750 027 500 + 1;
  • 2 750 027 500 ÷ 2 = 1 375 013 750 + 0;
  • 1 375 013 750 ÷ 2 = 687 506 875 + 0;
  • 687 506 875 ÷ 2 = 343 753 437 + 1;
  • 343 753 437 ÷ 2 = 171 876 718 + 1;
  • 171 876 718 ÷ 2 = 85 938 359 + 0;
  • 85 938 359 ÷ 2 = 42 969 179 + 1;
  • 42 969 179 ÷ 2 = 21 484 589 + 1;
  • 21 484 589 ÷ 2 = 10 742 294 + 1;
  • 10 742 294 ÷ 2 = 5 371 147 + 0;
  • 5 371 147 ÷ 2 = 2 685 573 + 1;
  • 2 685 573 ÷ 2 = 1 342 786 + 1;
  • 1 342 786 ÷ 2 = 671 393 + 0;
  • 671 393 ÷ 2 = 335 696 + 1;
  • 335 696 ÷ 2 = 167 848 + 0;
  • 167 848 ÷ 2 = 83 924 + 0;
  • 83 924 ÷ 2 = 41 962 + 0;
  • 41 962 ÷ 2 = 20 981 + 0;
  • 20 981 ÷ 2 = 10 490 + 1;
  • 10 490 ÷ 2 = 5 245 + 0;
  • 5 245 ÷ 2 = 2 622 + 1;
  • 2 622 ÷ 2 = 1 311 + 0;
  • 1 311 ÷ 2 = 655 + 1;
  • 655 ÷ 2 = 327 + 1;
  • 327 ÷ 2 = 163 + 1;
  • 163 ÷ 2 = 81 + 1;
  • 81 ÷ 2 = 40 + 1;
  • 40 ÷ 2 = 20 + 0;
  • 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 11 000 110 003(10), a positive integer number (with no sign),
converted from decimal system (from base 10)
and written as an unsigned binary (in base 2):

11 000 110 003(10) = 10 1000 1111 1010 1000 0101 1011 1011 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 11 000 110 002 converted from decimal system (from base 10) and written as an unsigned binary (in base 2) = ?

» Unsigned (positive) integer number 11 000 110 004 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)