Base Ten to Base Two: Unsigned Number 42 366 681 Converted and Written in Base Two. Natural Number (Positive Integer, No Sign) Converted From Decimal System to Binary Code

Base ten unsigned number 42 366 681(10) converted and written as a base two binary code

How to convert the base ten number 42 366 681 to base two:

  • A number written in base ten, or a decimal system number, is a number written using the digits 0 through 9. A number written in base two, or a binary system number, is a number written using only the digits 0 and 1.

  • To convert a base ten unsigned number (written in decimal system) to base two (written in binary), follow the steps below.

  • Divide the number repeatedly by 2: keep track of each remainder.
  • Stop when you get a quotient that is equal to zero.
  • Construct the base 2 representation of the positive number: take all the remainders starting from the bottom of the list constructed above.
  • Below you can see the conversion process to base two and the related calculations.

1. Divide the number repeatedly by 2:

Keep track of each remainder.

Stop when you get a quotient that is equal to zero.


  • division = quotient + remainder;
  • 42 366 681 ÷ 2 = 21 183 340 + 1;
  • 21 183 340 ÷ 2 = 10 591 670 + 0;
  • 10 591 670 ÷ 2 = 5 295 835 + 0;
  • 5 295 835 ÷ 2 = 2 647 917 + 1;
  • 2 647 917 ÷ 2 = 1 323 958 + 1;
  • 1 323 958 ÷ 2 = 661 979 + 0;
  • 661 979 ÷ 2 = 330 989 + 1;
  • 330 989 ÷ 2 = 165 494 + 1;
  • 165 494 ÷ 2 = 82 747 + 0;
  • 82 747 ÷ 2 = 41 373 + 1;
  • 41 373 ÷ 2 = 20 686 + 1;
  • 20 686 ÷ 2 = 10 343 + 0;
  • 10 343 ÷ 2 = 5 171 + 1;
  • 5 171 ÷ 2 = 2 585 + 1;
  • 2 585 ÷ 2 = 1 292 + 1;
  • 1 292 ÷ 2 = 646 + 0;
  • 646 ÷ 2 = 323 + 0;
  • 323 ÷ 2 = 161 + 1;
  • 161 ÷ 2 = 80 + 1;
  • 80 ÷ 2 = 40 + 0;
  • 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 42 366 681(10), a positive integer number (with no sign),
converted from decimal system (from base 10)
and written as an unsigned binary (in base 2):

42 366 681(10) = 10 1000 0110 0111 0110 1101 1001(2)

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

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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)