Unsigned: Integer ↗ Binary: 101 000 111 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 101 000 111(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;
  • 101 000 111 ÷ 2 = 50 500 055 + 1;
  • 50 500 055 ÷ 2 = 25 250 027 + 1;
  • 25 250 027 ÷ 2 = 12 625 013 + 1;
  • 12 625 013 ÷ 2 = 6 312 506 + 1;
  • 6 312 506 ÷ 2 = 3 156 253 + 0;
  • 3 156 253 ÷ 2 = 1 578 126 + 1;
  • 1 578 126 ÷ 2 = 789 063 + 0;
  • 789 063 ÷ 2 = 394 531 + 1;
  • 394 531 ÷ 2 = 197 265 + 1;
  • 197 265 ÷ 2 = 98 632 + 1;
  • 98 632 ÷ 2 = 49 316 + 0;
  • 49 316 ÷ 2 = 24 658 + 0;
  • 24 658 ÷ 2 = 12 329 + 0;
  • 12 329 ÷ 2 = 6 164 + 1;
  • 6 164 ÷ 2 = 3 082 + 0;
  • 3 082 ÷ 2 = 1 541 + 0;
  • 1 541 ÷ 2 = 770 + 1;
  • 770 ÷ 2 = 385 + 0;
  • 385 ÷ 2 = 192 + 1;
  • 192 ÷ 2 = 96 + 0;
  • 96 ÷ 2 = 48 + 0;
  • 48 ÷ 2 = 24 + 0;
  • 24 ÷ 2 = 12 + 0;
  • 12 ÷ 2 = 6 + 0;
  • 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 101 000 111(10), a positive integer number (with no sign),
converted from decimal system (from base 10)
and written as an unsigned binary (in base 2):

101 000 111(10) = 110 0000 0101 0010 0011 1010 1111(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 101 000 110 converted from decimal system (from base 10) and written as an unsigned binary (in base 2) = ?

» Unsigned (positive) integer number 101 000 112 converted from decimal system (from base 10) and written as an unsigned binary (in base 2) = ?

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All the decimal system (written in base ten) positive integers (with no sign) converted to unsigned binary (in base 2)

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)