Unsigned: Integer ↗ Binary: 10 000 101 013 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 10 000 101 013(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;
  • 10 000 101 013 ÷ 2 = 5 000 050 506 + 1;
  • 5 000 050 506 ÷ 2 = 2 500 025 253 + 0;
  • 2 500 025 253 ÷ 2 = 1 250 012 626 + 1;
  • 1 250 012 626 ÷ 2 = 625 006 313 + 0;
  • 625 006 313 ÷ 2 = 312 503 156 + 1;
  • 312 503 156 ÷ 2 = 156 251 578 + 0;
  • 156 251 578 ÷ 2 = 78 125 789 + 0;
  • 78 125 789 ÷ 2 = 39 062 894 + 1;
  • 39 062 894 ÷ 2 = 19 531 447 + 0;
  • 19 531 447 ÷ 2 = 9 765 723 + 1;
  • 9 765 723 ÷ 2 = 4 882 861 + 1;
  • 4 882 861 ÷ 2 = 2 441 430 + 1;
  • 2 441 430 ÷ 2 = 1 220 715 + 0;
  • 1 220 715 ÷ 2 = 610 357 + 1;
  • 610 357 ÷ 2 = 305 178 + 1;
  • 305 178 ÷ 2 = 152 589 + 0;
  • 152 589 ÷ 2 = 76 294 + 1;
  • 76 294 ÷ 2 = 38 147 + 0;
  • 38 147 ÷ 2 = 19 073 + 1;
  • 19 073 ÷ 2 = 9 536 + 1;
  • 9 536 ÷ 2 = 4 768 + 0;
  • 4 768 ÷ 2 = 2 384 + 0;
  • 2 384 ÷ 2 = 1 192 + 0;
  • 1 192 ÷ 2 = 596 + 0;
  • 596 ÷ 2 = 298 + 0;
  • 298 ÷ 2 = 149 + 0;
  • 149 ÷ 2 = 74 + 1;
  • 74 ÷ 2 = 37 + 0;
  • 37 ÷ 2 = 18 + 1;
  • 18 ÷ 2 = 9 + 0;
  • 9 ÷ 2 = 4 + 1;
  • 4 ÷ 2 = 2 + 0;
  • 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 10 000 101 013(10), a positive integer number (with no sign),
converted from decimal system (from base 10)
and written as an unsigned binary (in base 2):

10 000 101 013(10) = 10 0101 0100 0000 1101 0110 1110 1001 0101(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 10 000 101 012 converted from decimal system (from base 10) and written as an unsigned binary (in base 2) = ?

» Unsigned (positive) integer number 10 000 101 014 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)