Unsigned: Integer ↗ Binary: 101 111 011 000 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 101 111 011 000(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;
  • 101 111 011 000 ÷ 2 = 50 555 505 500 + 0;
  • 50 555 505 500 ÷ 2 = 25 277 752 750 + 0;
  • 25 277 752 750 ÷ 2 = 12 638 876 375 + 0;
  • 12 638 876 375 ÷ 2 = 6 319 438 187 + 1;
  • 6 319 438 187 ÷ 2 = 3 159 719 093 + 1;
  • 3 159 719 093 ÷ 2 = 1 579 859 546 + 1;
  • 1 579 859 546 ÷ 2 = 789 929 773 + 0;
  • 789 929 773 ÷ 2 = 394 964 886 + 1;
  • 394 964 886 ÷ 2 = 197 482 443 + 0;
  • 197 482 443 ÷ 2 = 98 741 221 + 1;
  • 98 741 221 ÷ 2 = 49 370 610 + 1;
  • 49 370 610 ÷ 2 = 24 685 305 + 0;
  • 24 685 305 ÷ 2 = 12 342 652 + 1;
  • 12 342 652 ÷ 2 = 6 171 326 + 0;
  • 6 171 326 ÷ 2 = 3 085 663 + 0;
  • 3 085 663 ÷ 2 = 1 542 831 + 1;
  • 1 542 831 ÷ 2 = 771 415 + 1;
  • 771 415 ÷ 2 = 385 707 + 1;
  • 385 707 ÷ 2 = 192 853 + 1;
  • 192 853 ÷ 2 = 96 426 + 1;
  • 96 426 ÷ 2 = 48 213 + 0;
  • 48 213 ÷ 2 = 24 106 + 1;
  • 24 106 ÷ 2 = 12 053 + 0;
  • 12 053 ÷ 2 = 6 026 + 1;
  • 6 026 ÷ 2 = 3 013 + 0;
  • 3 013 ÷ 2 = 1 506 + 1;
  • 1 506 ÷ 2 = 753 + 0;
  • 753 ÷ 2 = 376 + 1;
  • 376 ÷ 2 = 188 + 0;
  • 188 ÷ 2 = 94 + 0;
  • 94 ÷ 2 = 47 + 0;
  • 47 ÷ 2 = 23 + 1;
  • 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 101 111 011 000(10), a positive integer number (with no sign),
converted from decimal system (from base 10)
and written as an unsigned binary (in base 2):

101 111 011 000(10) = 1 0111 1000 1010 1010 1111 1001 0110 1011 1000(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)