Unsigned: Integer ↗ Binary: 5 470 379 403 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 5 470 379 403(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;
  • 5 470 379 403 ÷ 2 = 2 735 189 701 + 1;
  • 2 735 189 701 ÷ 2 = 1 367 594 850 + 1;
  • 1 367 594 850 ÷ 2 = 683 797 425 + 0;
  • 683 797 425 ÷ 2 = 341 898 712 + 1;
  • 341 898 712 ÷ 2 = 170 949 356 + 0;
  • 170 949 356 ÷ 2 = 85 474 678 + 0;
  • 85 474 678 ÷ 2 = 42 737 339 + 0;
  • 42 737 339 ÷ 2 = 21 368 669 + 1;
  • 21 368 669 ÷ 2 = 10 684 334 + 1;
  • 10 684 334 ÷ 2 = 5 342 167 + 0;
  • 5 342 167 ÷ 2 = 2 671 083 + 1;
  • 2 671 083 ÷ 2 = 1 335 541 + 1;
  • 1 335 541 ÷ 2 = 667 770 + 1;
  • 667 770 ÷ 2 = 333 885 + 0;
  • 333 885 ÷ 2 = 166 942 + 1;
  • 166 942 ÷ 2 = 83 471 + 0;
  • 83 471 ÷ 2 = 41 735 + 1;
  • 41 735 ÷ 2 = 20 867 + 1;
  • 20 867 ÷ 2 = 10 433 + 1;
  • 10 433 ÷ 2 = 5 216 + 1;
  • 5 216 ÷ 2 = 2 608 + 0;
  • 2 608 ÷ 2 = 1 304 + 0;
  • 1 304 ÷ 2 = 652 + 0;
  • 652 ÷ 2 = 326 + 0;
  • 326 ÷ 2 = 163 + 0;
  • 163 ÷ 2 = 81 + 1;
  • 81 ÷ 2 = 40 + 1;
  • 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 5 470 379 403(10), a positive integer number (with no sign),
converted from decimal system (from base 10)
and written as an unsigned binary (in base 2):

5 470 379 403(10) = 1 0100 0110 0000 1111 0101 1101 1000 1011(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 5 470 379 402 converted from decimal system (from base 10) and written as an unsigned binary (in base 2) = ?

» Unsigned (positive) integer number 5 470 379 404 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)