Unsigned: Integer ↗ Binary: 999 950 891 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 999 950 891(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;
  • 999 950 891 ÷ 2 = 499 975 445 + 1;
  • 499 975 445 ÷ 2 = 249 987 722 + 1;
  • 249 987 722 ÷ 2 = 124 993 861 + 0;
  • 124 993 861 ÷ 2 = 62 496 930 + 1;
  • 62 496 930 ÷ 2 = 31 248 465 + 0;
  • 31 248 465 ÷ 2 = 15 624 232 + 1;
  • 15 624 232 ÷ 2 = 7 812 116 + 0;
  • 7 812 116 ÷ 2 = 3 906 058 + 0;
  • 3 906 058 ÷ 2 = 1 953 029 + 0;
  • 1 953 029 ÷ 2 = 976 514 + 1;
  • 976 514 ÷ 2 = 488 257 + 0;
  • 488 257 ÷ 2 = 244 128 + 1;
  • 244 128 ÷ 2 = 122 064 + 0;
  • 122 064 ÷ 2 = 61 032 + 0;
  • 61 032 ÷ 2 = 30 516 + 0;
  • 30 516 ÷ 2 = 15 258 + 0;
  • 15 258 ÷ 2 = 7 629 + 0;
  • 7 629 ÷ 2 = 3 814 + 1;
  • 3 814 ÷ 2 = 1 907 + 0;
  • 1 907 ÷ 2 = 953 + 1;
  • 953 ÷ 2 = 476 + 1;
  • 476 ÷ 2 = 238 + 0;
  • 238 ÷ 2 = 119 + 0;
  • 119 ÷ 2 = 59 + 1;
  • 59 ÷ 2 = 29 + 1;
  • 29 ÷ 2 = 14 + 1;
  • 14 ÷ 2 = 7 + 0;
  • 7 ÷ 2 = 3 + 1;
  • 3 ÷ 2 = 1 + 1;
  • 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 999 950 891(10), a positive integer number (with no sign),
converted from decimal system (from base 10)
and written as an unsigned binary (in base 2):

999 950 891(10) = 11 1011 1001 1010 0000 1010 0010 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 999 950 890 converted from decimal system (from base 10) and written as an unsigned binary (in base 2) = ?

» Unsigned (positive) integer number 999 950 892 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)