Unsigned: Integer ↗ Binary: 10 000 000 000 016 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 10 000 000 000 016(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;
  • 10 000 000 000 016 ÷ 2 = 5 000 000 000 008 + 0;
  • 5 000 000 000 008 ÷ 2 = 2 500 000 000 004 + 0;
  • 2 500 000 000 004 ÷ 2 = 1 250 000 000 002 + 0;
  • 1 250 000 000 002 ÷ 2 = 625 000 000 001 + 0;
  • 625 000 000 001 ÷ 2 = 312 500 000 000 + 1;
  • 312 500 000 000 ÷ 2 = 156 250 000 000 + 0;
  • 156 250 000 000 ÷ 2 = 78 125 000 000 + 0;
  • 78 125 000 000 ÷ 2 = 39 062 500 000 + 0;
  • 39 062 500 000 ÷ 2 = 19 531 250 000 + 0;
  • 19 531 250 000 ÷ 2 = 9 765 625 000 + 0;
  • 9 765 625 000 ÷ 2 = 4 882 812 500 + 0;
  • 4 882 812 500 ÷ 2 = 2 441 406 250 + 0;
  • 2 441 406 250 ÷ 2 = 1 220 703 125 + 0;
  • 1 220 703 125 ÷ 2 = 610 351 562 + 1;
  • 610 351 562 ÷ 2 = 305 175 781 + 0;
  • 305 175 781 ÷ 2 = 152 587 890 + 1;
  • 152 587 890 ÷ 2 = 76 293 945 + 0;
  • 76 293 945 ÷ 2 = 38 146 972 + 1;
  • 38 146 972 ÷ 2 = 19 073 486 + 0;
  • 19 073 486 ÷ 2 = 9 536 743 + 0;
  • 9 536 743 ÷ 2 = 4 768 371 + 1;
  • 4 768 371 ÷ 2 = 2 384 185 + 1;
  • 2 384 185 ÷ 2 = 1 192 092 + 1;
  • 1 192 092 ÷ 2 = 596 046 + 0;
  • 596 046 ÷ 2 = 298 023 + 0;
  • 298 023 ÷ 2 = 149 011 + 1;
  • 149 011 ÷ 2 = 74 505 + 1;
  • 74 505 ÷ 2 = 37 252 + 1;
  • 37 252 ÷ 2 = 18 626 + 0;
  • 18 626 ÷ 2 = 9 313 + 0;
  • 9 313 ÷ 2 = 4 656 + 1;
  • 4 656 ÷ 2 = 2 328 + 0;
  • 2 328 ÷ 2 = 1 164 + 0;
  • 1 164 ÷ 2 = 582 + 0;
  • 582 ÷ 2 = 291 + 0;
  • 291 ÷ 2 = 145 + 1;
  • 145 ÷ 2 = 72 + 1;
  • 72 ÷ 2 = 36 + 0;
  • 36 ÷ 2 = 18 + 0;
  • 18 ÷ 2 = 9 + 0;
  • 9 ÷ 2 = 4 + 1;
  • 4 ÷ 2 = 2 + 0;
  • 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 10 000 000 000 016(10), a positive integer number (with no sign),
converted from decimal system (from base 10)
and written as an unsigned binary (in base 2):

10 000 000 000 016(10) = 1001 0001 1000 0100 1110 0111 0010 1010 0000 0001 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 10 000 000 000 015 converted from decimal system (from base 10) and written as an unsigned binary (in base 2) = ?

» Unsigned (positive) integer number 10 000 000 000 017 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)