Unsigned: Integer ↗ Binary: 10 110 011 037 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 10 110 011 037(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;
  • 10 110 011 037 ÷ 2 = 5 055 005 518 + 1;
  • 5 055 005 518 ÷ 2 = 2 527 502 759 + 0;
  • 2 527 502 759 ÷ 2 = 1 263 751 379 + 1;
  • 1 263 751 379 ÷ 2 = 631 875 689 + 1;
  • 631 875 689 ÷ 2 = 315 937 844 + 1;
  • 315 937 844 ÷ 2 = 157 968 922 + 0;
  • 157 968 922 ÷ 2 = 78 984 461 + 0;
  • 78 984 461 ÷ 2 = 39 492 230 + 1;
  • 39 492 230 ÷ 2 = 19 746 115 + 0;
  • 19 746 115 ÷ 2 = 9 873 057 + 1;
  • 9 873 057 ÷ 2 = 4 936 528 + 1;
  • 4 936 528 ÷ 2 = 2 468 264 + 0;
  • 2 468 264 ÷ 2 = 1 234 132 + 0;
  • 1 234 132 ÷ 2 = 617 066 + 0;
  • 617 066 ÷ 2 = 308 533 + 0;
  • 308 533 ÷ 2 = 154 266 + 1;
  • 154 266 ÷ 2 = 77 133 + 0;
  • 77 133 ÷ 2 = 38 566 + 1;
  • 38 566 ÷ 2 = 19 283 + 0;
  • 19 283 ÷ 2 = 9 641 + 1;
  • 9 641 ÷ 2 = 4 820 + 1;
  • 4 820 ÷ 2 = 2 410 + 0;
  • 2 410 ÷ 2 = 1 205 + 0;
  • 1 205 ÷ 2 = 602 + 1;
  • 602 ÷ 2 = 301 + 0;
  • 301 ÷ 2 = 150 + 1;
  • 150 ÷ 2 = 75 + 0;
  • 75 ÷ 2 = 37 + 1;
  • 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 10 110 011 037(10), a positive integer number (with no sign),
converted from decimal system (from base 10)
and written as an unsigned binary (in base 2):

10 110 011 037(10) = 10 0101 1010 1001 1010 1000 0110 1001 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 10 110 011 036 converted from decimal system (from base 10) and written as an unsigned binary (in base 2) = ?

» Unsigned (positive) integer number 10 110 011 038 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)