Unsigned: Integer ↗ Binary: 100 101 010 133 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 100 101 010 133(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;
  • 100 101 010 133 ÷ 2 = 50 050 505 066 + 1;
  • 50 050 505 066 ÷ 2 = 25 025 252 533 + 0;
  • 25 025 252 533 ÷ 2 = 12 512 626 266 + 1;
  • 12 512 626 266 ÷ 2 = 6 256 313 133 + 0;
  • 6 256 313 133 ÷ 2 = 3 128 156 566 + 1;
  • 3 128 156 566 ÷ 2 = 1 564 078 283 + 0;
  • 1 564 078 283 ÷ 2 = 782 039 141 + 1;
  • 782 039 141 ÷ 2 = 391 019 570 + 1;
  • 391 019 570 ÷ 2 = 195 509 785 + 0;
  • 195 509 785 ÷ 2 = 97 754 892 + 1;
  • 97 754 892 ÷ 2 = 48 877 446 + 0;
  • 48 877 446 ÷ 2 = 24 438 723 + 0;
  • 24 438 723 ÷ 2 = 12 219 361 + 1;
  • 12 219 361 ÷ 2 = 6 109 680 + 1;
  • 6 109 680 ÷ 2 = 3 054 840 + 0;
  • 3 054 840 ÷ 2 = 1 527 420 + 0;
  • 1 527 420 ÷ 2 = 763 710 + 0;
  • 763 710 ÷ 2 = 381 855 + 0;
  • 381 855 ÷ 2 = 190 927 + 1;
  • 190 927 ÷ 2 = 95 463 + 1;
  • 95 463 ÷ 2 = 47 731 + 1;
  • 47 731 ÷ 2 = 23 865 + 1;
  • 23 865 ÷ 2 = 11 932 + 1;
  • 11 932 ÷ 2 = 5 966 + 0;
  • 5 966 ÷ 2 = 2 983 + 0;
  • 2 983 ÷ 2 = 1 491 + 1;
  • 1 491 ÷ 2 = 745 + 1;
  • 745 ÷ 2 = 372 + 1;
  • 372 ÷ 2 = 186 + 0;
  • 186 ÷ 2 = 93 + 0;
  • 93 ÷ 2 = 46 + 1;
  • 46 ÷ 2 = 23 + 0;
  • 23 ÷ 2 = 11 + 1;
  • 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 100 101 010 133(10), a positive integer number (with no sign),
converted from decimal system (from base 10)
and written as an unsigned binary (in base 2):

100 101 010 133(10) = 1 0111 0100 1110 0111 1100 0011 0010 1101 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 100 101 010 132 converted from decimal system (from base 10) and written as an unsigned binary (in base 2) = ?

» Unsigned (positive) integer number 100 101 010 134 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)