Unsigned: Integer ↗ Binary: 999 999 893 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 999 999 893(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;
  • 999 999 893 ÷ 2 = 499 999 946 + 1;
  • 499 999 946 ÷ 2 = 249 999 973 + 0;
  • 249 999 973 ÷ 2 = 124 999 986 + 1;
  • 124 999 986 ÷ 2 = 62 499 993 + 0;
  • 62 499 993 ÷ 2 = 31 249 996 + 1;
  • 31 249 996 ÷ 2 = 15 624 998 + 0;
  • 15 624 998 ÷ 2 = 7 812 499 + 0;
  • 7 812 499 ÷ 2 = 3 906 249 + 1;
  • 3 906 249 ÷ 2 = 1 953 124 + 1;
  • 1 953 124 ÷ 2 = 976 562 + 0;
  • 976 562 ÷ 2 = 488 281 + 0;
  • 488 281 ÷ 2 = 244 140 + 1;
  • 244 140 ÷ 2 = 122 070 + 0;
  • 122 070 ÷ 2 = 61 035 + 0;
  • 61 035 ÷ 2 = 30 517 + 1;
  • 30 517 ÷ 2 = 15 258 + 1;
  • 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 999 999 893(10), a positive integer number (with no sign),
converted from decimal system (from base 10)
and written as an unsigned binary (in base 2):

999 999 893(10) = 11 1011 1001 1010 1100 1001 1001 0101(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 999 999 892 converted from decimal system (from base 10) and written as an unsigned binary (in base 2) = ?

» Unsigned (positive) integer number 999 999 894 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)