Unsigned: Integer ↗ Binary: 327 688 038 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 327 688 038(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;
  • 327 688 038 ÷ 2 = 163 844 019 + 0;
  • 163 844 019 ÷ 2 = 81 922 009 + 1;
  • 81 922 009 ÷ 2 = 40 961 004 + 1;
  • 40 961 004 ÷ 2 = 20 480 502 + 0;
  • 20 480 502 ÷ 2 = 10 240 251 + 0;
  • 10 240 251 ÷ 2 = 5 120 125 + 1;
  • 5 120 125 ÷ 2 = 2 560 062 + 1;
  • 2 560 062 ÷ 2 = 1 280 031 + 0;
  • 1 280 031 ÷ 2 = 640 015 + 1;
  • 640 015 ÷ 2 = 320 007 + 1;
  • 320 007 ÷ 2 = 160 003 + 1;
  • 160 003 ÷ 2 = 80 001 + 1;
  • 80 001 ÷ 2 = 40 000 + 1;
  • 40 000 ÷ 2 = 20 000 + 0;
  • 20 000 ÷ 2 = 10 000 + 0;
  • 10 000 ÷ 2 = 5 000 + 0;
  • 5 000 ÷ 2 = 2 500 + 0;
  • 2 500 ÷ 2 = 1 250 + 0;
  • 1 250 ÷ 2 = 625 + 0;
  • 625 ÷ 2 = 312 + 1;
  • 312 ÷ 2 = 156 + 0;
  • 156 ÷ 2 = 78 + 0;
  • 78 ÷ 2 = 39 + 0;
  • 39 ÷ 2 = 19 + 1;
  • 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 327 688 038(10), a positive integer number (with no sign),
converted from decimal system (from base 10)
and written as an unsigned binary (in base 2):

327 688 038(10) = 1 0011 1000 1000 0001 1111 0110 0110(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 327 688 037 converted from decimal system (from base 10) and written as an unsigned binary (in base 2) = ?

» Unsigned (positive) integer number 327 688 039 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)