Base Ten to Base Two: Unsigned Number 88 978 836 Converted and Written in Base Two. Natural Number (Positive Integer, No Sign) Converted From Decimal System to Binary Code

Base ten unsigned number 88 978 836(10) converted and written as a base two binary code

1. Divide the number repeatedly by 2:

Keep track of each remainder.

Stop when getting a quotient that is equal to zero.


  • division = quotient + remainder;
  • 88 978 836 ÷ 2 = 44 489 418 + 0;
  • 44 489 418 ÷ 2 = 22 244 709 + 0;
  • 22 244 709 ÷ 2 = 11 122 354 + 1;
  • 11 122 354 ÷ 2 = 5 561 177 + 0;
  • 5 561 177 ÷ 2 = 2 780 588 + 1;
  • 2 780 588 ÷ 2 = 1 390 294 + 0;
  • 1 390 294 ÷ 2 = 695 147 + 0;
  • 695 147 ÷ 2 = 347 573 + 1;
  • 347 573 ÷ 2 = 173 786 + 1;
  • 173 786 ÷ 2 = 86 893 + 0;
  • 86 893 ÷ 2 = 43 446 + 1;
  • 43 446 ÷ 2 = 21 723 + 0;
  • 21 723 ÷ 2 = 10 861 + 1;
  • 10 861 ÷ 2 = 5 430 + 1;
  • 5 430 ÷ 2 = 2 715 + 0;
  • 2 715 ÷ 2 = 1 357 + 1;
  • 1 357 ÷ 2 = 678 + 1;
  • 678 ÷ 2 = 339 + 0;
  • 339 ÷ 2 = 169 + 1;
  • 169 ÷ 2 = 84 + 1;
  • 84 ÷ 2 = 42 + 0;
  • 42 ÷ 2 = 21 + 0;
  • 21 ÷ 2 = 10 + 1;
  • 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 88 978 836(10), a positive integer number (with no sign),
converted from decimal system (from base 10)
and written as an unsigned binary (in base 2):

88 978 836(10) = 101 0100 1101 1011 0101 1001 0100(2)

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

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)