Unsigned: Integer ↗ Binary: 678 976 524 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 678 976 524(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;
  • 678 976 524 ÷ 2 = 339 488 262 + 0;
  • 339 488 262 ÷ 2 = 169 744 131 + 0;
  • 169 744 131 ÷ 2 = 84 872 065 + 1;
  • 84 872 065 ÷ 2 = 42 436 032 + 1;
  • 42 436 032 ÷ 2 = 21 218 016 + 0;
  • 21 218 016 ÷ 2 = 10 609 008 + 0;
  • 10 609 008 ÷ 2 = 5 304 504 + 0;
  • 5 304 504 ÷ 2 = 2 652 252 + 0;
  • 2 652 252 ÷ 2 = 1 326 126 + 0;
  • 1 326 126 ÷ 2 = 663 063 + 0;
  • 663 063 ÷ 2 = 331 531 + 1;
  • 331 531 ÷ 2 = 165 765 + 1;
  • 165 765 ÷ 2 = 82 882 + 1;
  • 82 882 ÷ 2 = 41 441 + 0;
  • 41 441 ÷ 2 = 20 720 + 1;
  • 20 720 ÷ 2 = 10 360 + 0;
  • 10 360 ÷ 2 = 5 180 + 0;
  • 5 180 ÷ 2 = 2 590 + 0;
  • 2 590 ÷ 2 = 1 295 + 0;
  • 1 295 ÷ 2 = 647 + 1;
  • 647 ÷ 2 = 323 + 1;
  • 323 ÷ 2 = 161 + 1;
  • 161 ÷ 2 = 80 + 1;
  • 80 ÷ 2 = 40 + 0;
  • 40 ÷ 2 = 20 + 0;
  • 20 ÷ 2 = 10 + 0;
  • 10 ÷ 2 = 5 + 0;
  • 5 ÷ 2 = 2 + 1;
  • 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 678 976 524(10), a positive integer number (with no sign),
converted from decimal system (from base 10)
and written as an unsigned binary (in base 2):

678 976 524(10) = 10 1000 0111 1000 0101 1100 0000 1100(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 678 976 523 converted from decimal system (from base 10) and written as an unsigned binary (in base 2) = ?

» Unsigned (positive) integer number 678 976 525 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)