Unsigned: Integer ↗ Binary: 42 510 000 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 42 510 000(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;
  • 42 510 000 ÷ 2 = 21 255 000 + 0;
  • 21 255 000 ÷ 2 = 10 627 500 + 0;
  • 10 627 500 ÷ 2 = 5 313 750 + 0;
  • 5 313 750 ÷ 2 = 2 656 875 + 0;
  • 2 656 875 ÷ 2 = 1 328 437 + 1;
  • 1 328 437 ÷ 2 = 664 218 + 1;
  • 664 218 ÷ 2 = 332 109 + 0;
  • 332 109 ÷ 2 = 166 054 + 1;
  • 166 054 ÷ 2 = 83 027 + 0;
  • 83 027 ÷ 2 = 41 513 + 1;
  • 41 513 ÷ 2 = 20 756 + 1;
  • 20 756 ÷ 2 = 10 378 + 0;
  • 10 378 ÷ 2 = 5 189 + 0;
  • 5 189 ÷ 2 = 2 594 + 1;
  • 2 594 ÷ 2 = 1 297 + 0;
  • 1 297 ÷ 2 = 648 + 1;
  • 648 ÷ 2 = 324 + 0;
  • 324 ÷ 2 = 162 + 0;
  • 162 ÷ 2 = 81 + 0;
  • 81 ÷ 2 = 40 + 1;
  • 40 ÷ 2 = 20 + 0;
  • 20 ÷ 2 = 10 + 0;
  • 10 ÷ 2 = 5 + 0;
  • 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 42 510 000(10), a positive integer number (with no sign),
converted from decimal system (from base 10)
and written as an unsigned binary (in base 2):

42 510 000(10) = 10 1000 1000 1010 0110 1011 0000(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 42 509 999 converted from decimal system (from base 10) and written as an unsigned binary (in base 2) = ?

» Unsigned (positive) integer number 42 510 001 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)