Unsigned: Integer ↗ Binary: 100 111 010 004 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 100 111 010 004(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;
  • 100 111 010 004 ÷ 2 = 50 055 505 002 + 0;
  • 50 055 505 002 ÷ 2 = 25 027 752 501 + 0;
  • 25 027 752 501 ÷ 2 = 12 513 876 250 + 1;
  • 12 513 876 250 ÷ 2 = 6 256 938 125 + 0;
  • 6 256 938 125 ÷ 2 = 3 128 469 062 + 1;
  • 3 128 469 062 ÷ 2 = 1 564 234 531 + 0;
  • 1 564 234 531 ÷ 2 = 782 117 265 + 1;
  • 782 117 265 ÷ 2 = 391 058 632 + 1;
  • 391 058 632 ÷ 2 = 195 529 316 + 0;
  • 195 529 316 ÷ 2 = 97 764 658 + 0;
  • 97 764 658 ÷ 2 = 48 882 329 + 0;
  • 48 882 329 ÷ 2 = 24 441 164 + 1;
  • 24 441 164 ÷ 2 = 12 220 582 + 0;
  • 12 220 582 ÷ 2 = 6 110 291 + 0;
  • 6 110 291 ÷ 2 = 3 055 145 + 1;
  • 3 055 145 ÷ 2 = 1 527 572 + 1;
  • 1 527 572 ÷ 2 = 763 786 + 0;
  • 763 786 ÷ 2 = 381 893 + 0;
  • 381 893 ÷ 2 = 190 946 + 1;
  • 190 946 ÷ 2 = 95 473 + 0;
  • 95 473 ÷ 2 = 47 736 + 1;
  • 47 736 ÷ 2 = 23 868 + 0;
  • 23 868 ÷ 2 = 11 934 + 0;
  • 11 934 ÷ 2 = 5 967 + 0;
  • 5 967 ÷ 2 = 2 983 + 1;
  • 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 100 111 010 004(10), a positive integer number (with no sign),
converted from decimal system (from base 10)
and written as an unsigned binary (in base 2):

100 111 010 004(10) = 1 0111 0100 1111 0001 0100 1100 1000 1101 0100(2)

Spaces were used to group digits: for binary, by 4, for decimal, by 3.

The latest positive (unsigned) integer numbers converted from decimal system (written in base ten) to unsigned binary (written in base two)

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)