Unsigned: Integer ↗ Binary: 100 100 101 110 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 100 100 101 110(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;
  • 100 100 101 110 ÷ 2 = 50 050 050 555 + 0;
  • 50 050 050 555 ÷ 2 = 25 025 025 277 + 1;
  • 25 025 025 277 ÷ 2 = 12 512 512 638 + 1;
  • 12 512 512 638 ÷ 2 = 6 256 256 319 + 0;
  • 6 256 256 319 ÷ 2 = 3 128 128 159 + 1;
  • 3 128 128 159 ÷ 2 = 1 564 064 079 + 1;
  • 1 564 064 079 ÷ 2 = 782 032 039 + 1;
  • 782 032 039 ÷ 2 = 391 016 019 + 1;
  • 391 016 019 ÷ 2 = 195 508 009 + 1;
  • 195 508 009 ÷ 2 = 97 754 004 + 1;
  • 97 754 004 ÷ 2 = 48 877 002 + 0;
  • 48 877 002 ÷ 2 = 24 438 501 + 0;
  • 24 438 501 ÷ 2 = 12 219 250 + 1;
  • 12 219 250 ÷ 2 = 6 109 625 + 0;
  • 6 109 625 ÷ 2 = 3 054 812 + 1;
  • 3 054 812 ÷ 2 = 1 527 406 + 0;
  • 1 527 406 ÷ 2 = 763 703 + 0;
  • 763 703 ÷ 2 = 381 851 + 1;
  • 381 851 ÷ 2 = 190 925 + 1;
  • 190 925 ÷ 2 = 95 462 + 1;
  • 95 462 ÷ 2 = 47 731 + 0;
  • 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 100 100 101 110(10), a positive integer number (with no sign),
converted from decimal system (from base 10)
and written as an unsigned binary (in base 2):

100 100 101 110(10) = 1 0111 0100 1110 0110 1110 0101 0011 1111 0110(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 100 100 101 109 converted from decimal system (from base 10) and written as an unsigned binary (in base 2) = ?

» Unsigned (positive) integer number 100 100 101 111 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)