Unsigned: Integer ↗ Binary: 1 011 000 096 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 1 011 000 096(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;
  • 1 011 000 096 ÷ 2 = 505 500 048 + 0;
  • 505 500 048 ÷ 2 = 252 750 024 + 0;
  • 252 750 024 ÷ 2 = 126 375 012 + 0;
  • 126 375 012 ÷ 2 = 63 187 506 + 0;
  • 63 187 506 ÷ 2 = 31 593 753 + 0;
  • 31 593 753 ÷ 2 = 15 796 876 + 1;
  • 15 796 876 ÷ 2 = 7 898 438 + 0;
  • 7 898 438 ÷ 2 = 3 949 219 + 0;
  • 3 949 219 ÷ 2 = 1 974 609 + 1;
  • 1 974 609 ÷ 2 = 987 304 + 1;
  • 987 304 ÷ 2 = 493 652 + 0;
  • 493 652 ÷ 2 = 246 826 + 0;
  • 246 826 ÷ 2 = 123 413 + 0;
  • 123 413 ÷ 2 = 61 706 + 1;
  • 61 706 ÷ 2 = 30 853 + 0;
  • 30 853 ÷ 2 = 15 426 + 1;
  • 15 426 ÷ 2 = 7 713 + 0;
  • 7 713 ÷ 2 = 3 856 + 1;
  • 3 856 ÷ 2 = 1 928 + 0;
  • 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 1 011 000 096(10), a positive integer number (with no sign),
converted from decimal system (from base 10)
and written as an unsigned binary (in base 2):

1 011 000 096(10) = 11 1100 0100 0010 1010 0011 0010 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 1 011 000 095 converted from decimal system (from base 10) and written as an unsigned binary (in base 2) = ?

» Unsigned (positive) integer number 1 011 000 097 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)