Unsigned: Integer ↗ Binary: 83 886 109 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 83 886 109(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;
  • 83 886 109 ÷ 2 = 41 943 054 + 1;
  • 41 943 054 ÷ 2 = 20 971 527 + 0;
  • 20 971 527 ÷ 2 = 10 485 763 + 1;
  • 10 485 763 ÷ 2 = 5 242 881 + 1;
  • 5 242 881 ÷ 2 = 2 621 440 + 1;
  • 2 621 440 ÷ 2 = 1 310 720 + 0;
  • 1 310 720 ÷ 2 = 655 360 + 0;
  • 655 360 ÷ 2 = 327 680 + 0;
  • 327 680 ÷ 2 = 163 840 + 0;
  • 163 840 ÷ 2 = 81 920 + 0;
  • 81 920 ÷ 2 = 40 960 + 0;
  • 40 960 ÷ 2 = 20 480 + 0;
  • 20 480 ÷ 2 = 10 240 + 0;
  • 10 240 ÷ 2 = 5 120 + 0;
  • 5 120 ÷ 2 = 2 560 + 0;
  • 2 560 ÷ 2 = 1 280 + 0;
  • 1 280 ÷ 2 = 640 + 0;
  • 640 ÷ 2 = 320 + 0;
  • 320 ÷ 2 = 160 + 0;
  • 160 ÷ 2 = 80 + 0;
  • 80 ÷ 2 = 40 + 0;
  • 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 83 886 109(10), a positive integer number (with no sign),
converted from decimal system (from base 10)
and written as an unsigned binary (in base 2):

83 886 109(10) = 101 0000 0000 0000 0000 0001 1101(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 83 886 108 converted from decimal system (from base 10) and written as an unsigned binary (in base 2) = ?

» Unsigned (positive) integer number 83 886 110 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)