Unsigned: Integer ↗ Binary: 1 100 101 101 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 1 100 101 101(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;
  • 1 100 101 101 ÷ 2 = 550 050 550 + 1;
  • 550 050 550 ÷ 2 = 275 025 275 + 0;
  • 275 025 275 ÷ 2 = 137 512 637 + 1;
  • 137 512 637 ÷ 2 = 68 756 318 + 1;
  • 68 756 318 ÷ 2 = 34 378 159 + 0;
  • 34 378 159 ÷ 2 = 17 189 079 + 1;
  • 17 189 079 ÷ 2 = 8 594 539 + 1;
  • 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 1 100 101 101(10), a positive integer number (with no sign),
converted from decimal system (from base 10)
and written as an unsigned binary (in base 2):

1 100 101 101(10) = 100 0001 1001 0010 0011 0101 1110 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 1 100 101 100 converted from decimal system (from base 10) and written as an unsigned binary (in base 2) = ?

» Unsigned (positive) integer number 1 100 101 102 converted from decimal system (from base 10) and written as an unsigned binary (in base 2) = ?

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All the decimal system (written in base ten) positive integers (with no sign) converted to unsigned binary (in base 2)

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)