Unsigned: Integer ↗ Binary: 110 111 111 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 110 111 111(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;
  • 110 111 111 ÷ 2 = 55 055 555 + 1;
  • 55 055 555 ÷ 2 = 27 527 777 + 1;
  • 27 527 777 ÷ 2 = 13 763 888 + 1;
  • 13 763 888 ÷ 2 = 6 881 944 + 0;
  • 6 881 944 ÷ 2 = 3 440 972 + 0;
  • 3 440 972 ÷ 2 = 1 720 486 + 0;
  • 1 720 486 ÷ 2 = 860 243 + 0;
  • 860 243 ÷ 2 = 430 121 + 1;
  • 430 121 ÷ 2 = 215 060 + 1;
  • 215 060 ÷ 2 = 107 530 + 0;
  • 107 530 ÷ 2 = 53 765 + 0;
  • 53 765 ÷ 2 = 26 882 + 1;
  • 26 882 ÷ 2 = 13 441 + 0;
  • 13 441 ÷ 2 = 6 720 + 1;
  • 6 720 ÷ 2 = 3 360 + 0;
  • 3 360 ÷ 2 = 1 680 + 0;
  • 1 680 ÷ 2 = 840 + 0;
  • 840 ÷ 2 = 420 + 0;
  • 420 ÷ 2 = 210 + 0;
  • 210 ÷ 2 = 105 + 0;
  • 105 ÷ 2 = 52 + 1;
  • 52 ÷ 2 = 26 + 0;
  • 26 ÷ 2 = 13 + 0;
  • 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 number:

Take all the remainders starting from the bottom of the list constructed above.


Number 110 111 111(10), a positive integer number (with no sign),
converted from decimal system (from base 10)
and written as an unsigned binary (in base 2):

110 111 111(10) = 110 1001 0000 0010 1001 1000 0111(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)