Unsigned: Integer ↗ Binary: 642 587 447 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 642 587 447(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;
  • 642 587 447 ÷ 2 = 321 293 723 + 1;
  • 321 293 723 ÷ 2 = 160 646 861 + 1;
  • 160 646 861 ÷ 2 = 80 323 430 + 1;
  • 80 323 430 ÷ 2 = 40 161 715 + 0;
  • 40 161 715 ÷ 2 = 20 080 857 + 1;
  • 20 080 857 ÷ 2 = 10 040 428 + 1;
  • 10 040 428 ÷ 2 = 5 020 214 + 0;
  • 5 020 214 ÷ 2 = 2 510 107 + 0;
  • 2 510 107 ÷ 2 = 1 255 053 + 1;
  • 1 255 053 ÷ 2 = 627 526 + 1;
  • 627 526 ÷ 2 = 313 763 + 0;
  • 313 763 ÷ 2 = 156 881 + 1;
  • 156 881 ÷ 2 = 78 440 + 1;
  • 78 440 ÷ 2 = 39 220 + 0;
  • 39 220 ÷ 2 = 19 610 + 0;
  • 19 610 ÷ 2 = 9 805 + 0;
  • 9 805 ÷ 2 = 4 902 + 1;
  • 4 902 ÷ 2 = 2 451 + 0;
  • 2 451 ÷ 2 = 1 225 + 1;
  • 1 225 ÷ 2 = 612 + 1;
  • 612 ÷ 2 = 306 + 0;
  • 306 ÷ 2 = 153 + 0;
  • 153 ÷ 2 = 76 + 1;
  • 76 ÷ 2 = 38 + 0;
  • 38 ÷ 2 = 19 + 0;
  • 19 ÷ 2 = 9 + 1;
  • 9 ÷ 2 = 4 + 1;
  • 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 642 587 447(10), a positive integer number (with no sign),
converted from decimal system (from base 10)
and written as an unsigned binary (in base 2):

642 587 447(10) = 10 0110 0100 1101 0001 1011 0011 0111(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 642 587 446 converted from decimal system (from base 10) and written as an unsigned binary (in base 2) = ?

» Unsigned (positive) integer number 642 587 448 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)