Unsigned: Integer ↗ Binary: 1 011 111 216 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 1 011 111 216(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;
  • 1 011 111 216 ÷ 2 = 505 555 608 + 0;
  • 505 555 608 ÷ 2 = 252 777 804 + 0;
  • 252 777 804 ÷ 2 = 126 388 902 + 0;
  • 126 388 902 ÷ 2 = 63 194 451 + 0;
  • 63 194 451 ÷ 2 = 31 597 225 + 1;
  • 31 597 225 ÷ 2 = 15 798 612 + 1;
  • 15 798 612 ÷ 2 = 7 899 306 + 0;
  • 7 899 306 ÷ 2 = 3 949 653 + 0;
  • 3 949 653 ÷ 2 = 1 974 826 + 1;
  • 1 974 826 ÷ 2 = 987 413 + 0;
  • 987 413 ÷ 2 = 493 706 + 1;
  • 493 706 ÷ 2 = 246 853 + 0;
  • 246 853 ÷ 2 = 123 426 + 1;
  • 123 426 ÷ 2 = 61 713 + 0;
  • 61 713 ÷ 2 = 30 856 + 1;
  • 30 856 ÷ 2 = 15 428 + 0;
  • 15 428 ÷ 2 = 7 714 + 0;
  • 7 714 ÷ 2 = 3 857 + 0;
  • 3 857 ÷ 2 = 1 928 + 1;
  • 1 928 ÷ 2 = 964 + 0;
  • 964 ÷ 2 = 482 + 0;
  • 482 ÷ 2 = 241 + 0;
  • 241 ÷ 2 = 120 + 1;
  • 120 ÷ 2 = 60 + 0;
  • 60 ÷ 2 = 30 + 0;
  • 30 ÷ 2 = 15 + 0;
  • 15 ÷ 2 = 7 + 1;
  • 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 1 011 111 216(10), a positive integer number (with no sign),
converted from decimal system (from base 10)
and written as an unsigned binary (in base 2):

1 011 111 216(10) = 11 1100 0100 0100 0101 0101 0011 0000(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 1 011 111 215 converted from decimal system (from base 10) and written as an unsigned binary (in base 2) = ?

» Unsigned (positive) integer number 1 011 111 217 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)