Base Ten to Base Two: Unsigned Number 385 935 994 Converted and Written in Base Two. Natural Number (Positive Integer, No Sign) Converted From Decimal System to Binary Code

Base ten unsigned number 385 935 994(10) converted and written as a base two binary code

How to convert the base ten number 385 935 994 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;
  • 385 935 994 ÷ 2 = 192 967 997 + 0;
  • 192 967 997 ÷ 2 = 96 483 998 + 1;
  • 96 483 998 ÷ 2 = 48 241 999 + 0;
  • 48 241 999 ÷ 2 = 24 120 999 + 1;
  • 24 120 999 ÷ 2 = 12 060 499 + 1;
  • 12 060 499 ÷ 2 = 6 030 249 + 1;
  • 6 030 249 ÷ 2 = 3 015 124 + 1;
  • 3 015 124 ÷ 2 = 1 507 562 + 0;
  • 1 507 562 ÷ 2 = 753 781 + 0;
  • 753 781 ÷ 2 = 376 890 + 1;
  • 376 890 ÷ 2 = 188 445 + 0;
  • 188 445 ÷ 2 = 94 222 + 1;
  • 94 222 ÷ 2 = 47 111 + 0;
  • 47 111 ÷ 2 = 23 555 + 1;
  • 23 555 ÷ 2 = 11 777 + 1;
  • 11 777 ÷ 2 = 5 888 + 1;
  • 5 888 ÷ 2 = 2 944 + 0;
  • 2 944 ÷ 2 = 1 472 + 0;
  • 1 472 ÷ 2 = 736 + 0;
  • 736 ÷ 2 = 368 + 0;
  • 368 ÷ 2 = 184 + 0;
  • 184 ÷ 2 = 92 + 0;
  • 92 ÷ 2 = 46 + 0;
  • 46 ÷ 2 = 23 + 0;
  • 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 385 935 994(10), a positive integer number (with no sign),
converted from decimal system (from base 10)
and written as an unsigned binary (in base 2):

385 935 994 (base 10) = 1 0111 0000 0000 1110 1010 0111 1010 (base 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)