Base Ten to Base Two: Unsigned Number 125 833 223 Converted and Written in Base Two. Natural Number (Positive Integer, No Sign) Converted From Decimal System to Binary Code

Base ten unsigned number 125 833 223(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;
  • 125 833 223 ÷ 2 = 62 916 611 + 1;
  • 62 916 611 ÷ 2 = 31 458 305 + 1;
  • 31 458 305 ÷ 2 = 15 729 152 + 1;
  • 15 729 152 ÷ 2 = 7 864 576 + 0;
  • 7 864 576 ÷ 2 = 3 932 288 + 0;
  • 3 932 288 ÷ 2 = 1 966 144 + 0;
  • 1 966 144 ÷ 2 = 983 072 + 0;
  • 983 072 ÷ 2 = 491 536 + 0;
  • 491 536 ÷ 2 = 245 768 + 0;
  • 245 768 ÷ 2 = 122 884 + 0;
  • 122 884 ÷ 2 = 61 442 + 0;
  • 61 442 ÷ 2 = 30 721 + 0;
  • 30 721 ÷ 2 = 15 360 + 1;
  • 15 360 ÷ 2 = 7 680 + 0;
  • 7 680 ÷ 2 = 3 840 + 0;
  • 3 840 ÷ 2 = 1 920 + 0;
  • 1 920 ÷ 2 = 960 + 0;
  • 960 ÷ 2 = 480 + 0;
  • 480 ÷ 2 = 240 + 0;
  • 240 ÷ 2 = 120 + 0;
  • 120 ÷ 2 = 60 + 0;
  • 60 ÷ 2 = 30 + 0;
  • 30 ÷ 2 = 15 + 0;
  • 15 ÷ 2 = 7 + 1;
  • 7 ÷ 2 = 3 + 1;
  • 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 125 833 223(10), a positive integer number (with no sign),
converted from decimal system (from base 10)
and written as an unsigned binary (in base 2):

125 833 223(10) = 111 1000 0000 0001 0000 0000 0111(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)