Unsigned: Integer ↗ Binary: 1 111 010 076 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 1 111 010 076(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;
  • 1 111 010 076 ÷ 2 = 555 505 038 + 0;
  • 555 505 038 ÷ 2 = 277 752 519 + 0;
  • 277 752 519 ÷ 2 = 138 876 259 + 1;
  • 138 876 259 ÷ 2 = 69 438 129 + 1;
  • 69 438 129 ÷ 2 = 34 719 064 + 1;
  • 34 719 064 ÷ 2 = 17 359 532 + 0;
  • 17 359 532 ÷ 2 = 8 679 766 + 0;
  • 8 679 766 ÷ 2 = 4 339 883 + 0;
  • 4 339 883 ÷ 2 = 2 169 941 + 1;
  • 2 169 941 ÷ 2 = 1 084 970 + 1;
  • 1 084 970 ÷ 2 = 542 485 + 0;
  • 542 485 ÷ 2 = 271 242 + 1;
  • 271 242 ÷ 2 = 135 621 + 0;
  • 135 621 ÷ 2 = 67 810 + 1;
  • 67 810 ÷ 2 = 33 905 + 0;
  • 33 905 ÷ 2 = 16 952 + 1;
  • 16 952 ÷ 2 = 8 476 + 0;
  • 8 476 ÷ 2 = 4 238 + 0;
  • 4 238 ÷ 2 = 2 119 + 0;
  • 2 119 ÷ 2 = 1 059 + 1;
  • 1 059 ÷ 2 = 529 + 1;
  • 529 ÷ 2 = 264 + 1;
  • 264 ÷ 2 = 132 + 0;
  • 132 ÷ 2 = 66 + 0;
  • 66 ÷ 2 = 33 + 0;
  • 33 ÷ 2 = 16 + 1;
  • 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 1 111 010 076(10), a positive integer number (with no sign),
converted from decimal system (from base 10)
and written as an unsigned binary (in base 2):

1 111 010 076(10) = 100 0010 0011 1000 1010 1011 0001 1100(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)