Unsigned: Integer ↗ Binary: 1 500 000 001 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 1 500 000 001(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;
  • 1 500 000 001 ÷ 2 = 750 000 000 + 1;
  • 750 000 000 ÷ 2 = 375 000 000 + 0;
  • 375 000 000 ÷ 2 = 187 500 000 + 0;
  • 187 500 000 ÷ 2 = 93 750 000 + 0;
  • 93 750 000 ÷ 2 = 46 875 000 + 0;
  • 46 875 000 ÷ 2 = 23 437 500 + 0;
  • 23 437 500 ÷ 2 = 11 718 750 + 0;
  • 11 718 750 ÷ 2 = 5 859 375 + 0;
  • 5 859 375 ÷ 2 = 2 929 687 + 1;
  • 2 929 687 ÷ 2 = 1 464 843 + 1;
  • 1 464 843 ÷ 2 = 732 421 + 1;
  • 732 421 ÷ 2 = 366 210 + 1;
  • 366 210 ÷ 2 = 183 105 + 0;
  • 183 105 ÷ 2 = 91 552 + 1;
  • 91 552 ÷ 2 = 45 776 + 0;
  • 45 776 ÷ 2 = 22 888 + 0;
  • 22 888 ÷ 2 = 11 444 + 0;
  • 11 444 ÷ 2 = 5 722 + 0;
  • 5 722 ÷ 2 = 2 861 + 0;
  • 2 861 ÷ 2 = 1 430 + 1;
  • 1 430 ÷ 2 = 715 + 0;
  • 715 ÷ 2 = 357 + 1;
  • 357 ÷ 2 = 178 + 1;
  • 178 ÷ 2 = 89 + 0;
  • 89 ÷ 2 = 44 + 1;
  • 44 ÷ 2 = 22 + 0;
  • 22 ÷ 2 = 11 + 0;
  • 11 ÷ 2 = 5 + 1;
  • 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 1 500 000 001(10), a positive integer number (with no sign),
converted from decimal system (from base 10)
and written as an unsigned binary (in base 2):

1 500 000 001(10) = 101 1001 0110 1000 0010 1111 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 1 500 000 000 converted from decimal system (from base 10) and written as an unsigned binary (in base 2) = ?

» Unsigned (positive) integer number 1 500 000 002 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)