Unsigned: Integer ↗ Binary: 1 100 101 011 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 1 100 101 011(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;
  • 1 100 101 011 ÷ 2 = 550 050 505 + 1;
  • 550 050 505 ÷ 2 = 275 025 252 + 1;
  • 275 025 252 ÷ 2 = 137 512 626 + 0;
  • 137 512 626 ÷ 2 = 68 756 313 + 0;
  • 68 756 313 ÷ 2 = 34 378 156 + 1;
  • 34 378 156 ÷ 2 = 17 189 078 + 0;
  • 17 189 078 ÷ 2 = 8 594 539 + 0;
  • 8 594 539 ÷ 2 = 4 297 269 + 1;
  • 4 297 269 ÷ 2 = 2 148 634 + 1;
  • 2 148 634 ÷ 2 = 1 074 317 + 0;
  • 1 074 317 ÷ 2 = 537 158 + 1;
  • 537 158 ÷ 2 = 268 579 + 0;
  • 268 579 ÷ 2 = 134 289 + 1;
  • 134 289 ÷ 2 = 67 144 + 1;
  • 67 144 ÷ 2 = 33 572 + 0;
  • 33 572 ÷ 2 = 16 786 + 0;
  • 16 786 ÷ 2 = 8 393 + 0;
  • 8 393 ÷ 2 = 4 196 + 1;
  • 4 196 ÷ 2 = 2 098 + 0;
  • 2 098 ÷ 2 = 1 049 + 0;
  • 1 049 ÷ 2 = 524 + 1;
  • 524 ÷ 2 = 262 + 0;
  • 262 ÷ 2 = 131 + 0;
  • 131 ÷ 2 = 65 + 1;
  • 65 ÷ 2 = 32 + 1;
  • 32 ÷ 2 = 16 + 0;
  • 16 ÷ 2 = 8 + 0;
  • 8 ÷ 2 = 4 + 0;
  • 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 1 100 101 011(10), a positive integer number (with no sign),
converted from decimal system (from base 10)
and written as an unsigned binary (in base 2):

1 100 101 011(10) = 100 0001 1001 0010 0011 0101 1001 0011(2)

Spaces were used to group digits: for binary, by 4, for decimal, by 3.

The latest positive (unsigned) integer numbers converted from decimal system (written in base ten) to unsigned binary (written in base two)

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)