Unsigned: Integer ↗ Binary: 100 010 011 108 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 100 010 011 108(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;
  • 100 010 011 108 ÷ 2 = 50 005 005 554 + 0;
  • 50 005 005 554 ÷ 2 = 25 002 502 777 + 0;
  • 25 002 502 777 ÷ 2 = 12 501 251 388 + 1;
  • 12 501 251 388 ÷ 2 = 6 250 625 694 + 0;
  • 6 250 625 694 ÷ 2 = 3 125 312 847 + 0;
  • 3 125 312 847 ÷ 2 = 1 562 656 423 + 1;
  • 1 562 656 423 ÷ 2 = 781 328 211 + 1;
  • 781 328 211 ÷ 2 = 390 664 105 + 1;
  • 390 664 105 ÷ 2 = 195 332 052 + 1;
  • 195 332 052 ÷ 2 = 97 666 026 + 0;
  • 97 666 026 ÷ 2 = 48 833 013 + 0;
  • 48 833 013 ÷ 2 = 24 416 506 + 1;
  • 24 416 506 ÷ 2 = 12 208 253 + 0;
  • 12 208 253 ÷ 2 = 6 104 126 + 1;
  • 6 104 126 ÷ 2 = 3 052 063 + 0;
  • 3 052 063 ÷ 2 = 1 526 031 + 1;
  • 1 526 031 ÷ 2 = 763 015 + 1;
  • 763 015 ÷ 2 = 381 507 + 1;
  • 381 507 ÷ 2 = 190 753 + 1;
  • 190 753 ÷ 2 = 95 376 + 1;
  • 95 376 ÷ 2 = 47 688 + 0;
  • 47 688 ÷ 2 = 23 844 + 0;
  • 23 844 ÷ 2 = 11 922 + 0;
  • 11 922 ÷ 2 = 5 961 + 0;
  • 5 961 ÷ 2 = 2 980 + 1;
  • 2 980 ÷ 2 = 1 490 + 0;
  • 1 490 ÷ 2 = 745 + 0;
  • 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 100 010 011 108(10), a positive integer number (with no sign),
converted from decimal system (from base 10)
and written as an unsigned binary (in base 2):

100 010 011 108(10) = 1 0111 0100 1001 0000 1111 1010 1001 1110 0100(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 100 010 011 107 converted from decimal system (from base 10) and written as an unsigned binary (in base 2) = ?

» Unsigned (positive) integer number 100 010 011 109 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)