Unsigned: Integer ↗ Binary: 40 000 082 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 40 000 082(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;
  • 40 000 082 ÷ 2 = 20 000 041 + 0;
  • 20 000 041 ÷ 2 = 10 000 020 + 1;
  • 10 000 020 ÷ 2 = 5 000 010 + 0;
  • 5 000 010 ÷ 2 = 2 500 005 + 0;
  • 2 500 005 ÷ 2 = 1 250 002 + 1;
  • 1 250 002 ÷ 2 = 625 001 + 0;
  • 625 001 ÷ 2 = 312 500 + 1;
  • 312 500 ÷ 2 = 156 250 + 0;
  • 156 250 ÷ 2 = 78 125 + 0;
  • 78 125 ÷ 2 = 39 062 + 1;
  • 39 062 ÷ 2 = 19 531 + 0;
  • 19 531 ÷ 2 = 9 765 + 1;
  • 9 765 ÷ 2 = 4 882 + 1;
  • 4 882 ÷ 2 = 2 441 + 0;
  • 2 441 ÷ 2 = 1 220 + 1;
  • 1 220 ÷ 2 = 610 + 0;
  • 610 ÷ 2 = 305 + 0;
  • 305 ÷ 2 = 152 + 1;
  • 152 ÷ 2 = 76 + 0;
  • 76 ÷ 2 = 38 + 0;
  • 38 ÷ 2 = 19 + 0;
  • 19 ÷ 2 = 9 + 1;
  • 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 40 000 082(10), a positive integer number (with no sign),
converted from decimal system (from base 10)
and written as an unsigned binary (in base 2):

40 000 082(10) = 10 0110 0010 0101 1010 0101 0010(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 40 000 081 converted from decimal system (from base 10) and written as an unsigned binary (in base 2) = ?

» Unsigned (positive) integer number 40 000 083 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)