Unsigned: Integer ↗ Binary: 2 000 000 001 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 2 000 000 001(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;
  • 2 000 000 001 ÷ 2 = 1 000 000 000 + 1;
  • 1 000 000 000 ÷ 2 = 500 000 000 + 0;
  • 500 000 000 ÷ 2 = 250 000 000 + 0;
  • 250 000 000 ÷ 2 = 125 000 000 + 0;
  • 125 000 000 ÷ 2 = 62 500 000 + 0;
  • 62 500 000 ÷ 2 = 31 250 000 + 0;
  • 31 250 000 ÷ 2 = 15 625 000 + 0;
  • 15 625 000 ÷ 2 = 7 812 500 + 0;
  • 7 812 500 ÷ 2 = 3 906 250 + 0;
  • 3 906 250 ÷ 2 = 1 953 125 + 0;
  • 1 953 125 ÷ 2 = 976 562 + 1;
  • 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 2 000 000 001(10), a positive integer number (with no sign),
converted from decimal system (from base 10)
and written as an unsigned binary (in base 2):

2 000 000 001(10) = 111 0111 0011 0101 1001 0100 0000 0001(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 2 000 000 000 converted from decimal system (from base 10) and written as an unsigned binary (in base 2) = ?

» Unsigned (positive) integer number 2 000 000 002 converted from decimal system (from base 10) and written as an unsigned binary (in base 2) = ?

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All the decimal system (written in base ten) positive integers (with no sign) converted to unsigned binary (in base 2)

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)