Unsigned: Integer ↗ Binary: 110 101 011 102 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 110 101 011 102(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;
  • 110 101 011 102 ÷ 2 = 55 050 505 551 + 0;
  • 55 050 505 551 ÷ 2 = 27 525 252 775 + 1;
  • 27 525 252 775 ÷ 2 = 13 762 626 387 + 1;
  • 13 762 626 387 ÷ 2 = 6 881 313 193 + 1;
  • 6 881 313 193 ÷ 2 = 3 440 656 596 + 1;
  • 3 440 656 596 ÷ 2 = 1 720 328 298 + 0;
  • 1 720 328 298 ÷ 2 = 860 164 149 + 0;
  • 860 164 149 ÷ 2 = 430 082 074 + 1;
  • 430 082 074 ÷ 2 = 215 041 037 + 0;
  • 215 041 037 ÷ 2 = 107 520 518 + 1;
  • 107 520 518 ÷ 2 = 53 760 259 + 0;
  • 53 760 259 ÷ 2 = 26 880 129 + 1;
  • 26 880 129 ÷ 2 = 13 440 064 + 1;
  • 13 440 064 ÷ 2 = 6 720 032 + 0;
  • 6 720 032 ÷ 2 = 3 360 016 + 0;
  • 3 360 016 ÷ 2 = 1 680 008 + 0;
  • 1 680 008 ÷ 2 = 840 004 + 0;
  • 840 004 ÷ 2 = 420 002 + 0;
  • 420 002 ÷ 2 = 210 001 + 0;
  • 210 001 ÷ 2 = 105 000 + 1;
  • 105 000 ÷ 2 = 52 500 + 0;
  • 52 500 ÷ 2 = 26 250 + 0;
  • 26 250 ÷ 2 = 13 125 + 0;
  • 13 125 ÷ 2 = 6 562 + 1;
  • 6 562 ÷ 2 = 3 281 + 0;
  • 3 281 ÷ 2 = 1 640 + 1;
  • 1 640 ÷ 2 = 820 + 0;
  • 820 ÷ 2 = 410 + 0;
  • 410 ÷ 2 = 205 + 0;
  • 205 ÷ 2 = 102 + 1;
  • 102 ÷ 2 = 51 + 0;
  • 51 ÷ 2 = 25 + 1;
  • 25 ÷ 2 = 12 + 1;
  • 12 ÷ 2 = 6 + 0;
  • 6 ÷ 2 = 3 + 0;
  • 3 ÷ 2 = 1 + 1;
  • 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 110 101 011 102(10), a positive integer number (with no sign),
converted from decimal system (from base 10)
and written as an unsigned binary (in base 2):

110 101 011 102(10) = 1 1001 1010 0010 1000 1000 0001 1010 1001 1110(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 110 101 011 101 converted from decimal system (from base 10) and written as an unsigned binary (in base 2) = ?

» Unsigned (positive) integer number 110 101 011 103 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)