Unsigned: Integer ↗ Binary: 11 011 000 011 011 013 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 11 011 000 011 011 013(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;
  • 11 011 000 011 011 013 ÷ 2 = 5 505 500 005 505 506 + 1;
  • 5 505 500 005 505 506 ÷ 2 = 2 752 750 002 752 753 + 0;
  • 2 752 750 002 752 753 ÷ 2 = 1 376 375 001 376 376 + 1;
  • 1 376 375 001 376 376 ÷ 2 = 688 187 500 688 188 + 0;
  • 688 187 500 688 188 ÷ 2 = 344 093 750 344 094 + 0;
  • 344 093 750 344 094 ÷ 2 = 172 046 875 172 047 + 0;
  • 172 046 875 172 047 ÷ 2 = 86 023 437 586 023 + 1;
  • 86 023 437 586 023 ÷ 2 = 43 011 718 793 011 + 1;
  • 43 011 718 793 011 ÷ 2 = 21 505 859 396 505 + 1;
  • 21 505 859 396 505 ÷ 2 = 10 752 929 698 252 + 1;
  • 10 752 929 698 252 ÷ 2 = 5 376 464 849 126 + 0;
  • 5 376 464 849 126 ÷ 2 = 2 688 232 424 563 + 0;
  • 2 688 232 424 563 ÷ 2 = 1 344 116 212 281 + 1;
  • 1 344 116 212 281 ÷ 2 = 672 058 106 140 + 1;
  • 672 058 106 140 ÷ 2 = 336 029 053 070 + 0;
  • 336 029 053 070 ÷ 2 = 168 014 526 535 + 0;
  • 168 014 526 535 ÷ 2 = 84 007 263 267 + 1;
  • 84 007 263 267 ÷ 2 = 42 003 631 633 + 1;
  • 42 003 631 633 ÷ 2 = 21 001 815 816 + 1;
  • 21 001 815 816 ÷ 2 = 10 500 907 908 + 0;
  • 10 500 907 908 ÷ 2 = 5 250 453 954 + 0;
  • 5 250 453 954 ÷ 2 = 2 625 226 977 + 0;
  • 2 625 226 977 ÷ 2 = 1 312 613 488 + 1;
  • 1 312 613 488 ÷ 2 = 656 306 744 + 0;
  • 656 306 744 ÷ 2 = 328 153 372 + 0;
  • 328 153 372 ÷ 2 = 164 076 686 + 0;
  • 164 076 686 ÷ 2 = 82 038 343 + 0;
  • 82 038 343 ÷ 2 = 41 019 171 + 1;
  • 41 019 171 ÷ 2 = 20 509 585 + 1;
  • 20 509 585 ÷ 2 = 10 254 792 + 1;
  • 10 254 792 ÷ 2 = 5 127 396 + 0;
  • 5 127 396 ÷ 2 = 2 563 698 + 0;
  • 2 563 698 ÷ 2 = 1 281 849 + 0;
  • 1 281 849 ÷ 2 = 640 924 + 1;
  • 640 924 ÷ 2 = 320 462 + 0;
  • 320 462 ÷ 2 = 160 231 + 0;
  • 160 231 ÷ 2 = 80 115 + 1;
  • 80 115 ÷ 2 = 40 057 + 1;
  • 40 057 ÷ 2 = 20 028 + 1;
  • 20 028 ÷ 2 = 10 014 + 0;
  • 10 014 ÷ 2 = 5 007 + 0;
  • 5 007 ÷ 2 = 2 503 + 1;
  • 2 503 ÷ 2 = 1 251 + 1;
  • 1 251 ÷ 2 = 625 + 1;
  • 625 ÷ 2 = 312 + 1;
  • 312 ÷ 2 = 156 + 0;
  • 156 ÷ 2 = 78 + 0;
  • 78 ÷ 2 = 39 + 0;
  • 39 ÷ 2 = 19 + 1;
  • 19 ÷ 2 = 9 + 1;
  • 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 11 011 000 011 011 013(10), a positive integer number (with no sign),
converted from decimal system (from base 10)
and written as an unsigned binary (in base 2):

11 011 000 011 011 013(10) = 10 0111 0001 1110 0111 0010 0011 1000 0100 0111 0011 0011 1100 0101(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 11 011 000 011 011 012 converted from decimal system (from base 10) and written as an unsigned binary (in base 2) = ?

» Unsigned (positive) integer number 11 011 000 011 011 014 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)