Base Ten to Base Two: Unsigned Number 12 345 537 Converted and Written in Base Two. Natural Number (Positive Integer, No Sign) Converted From Decimal System to Binary Code

Base ten unsigned number 12 345 537(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;
  • 12 345 537 ÷ 2 = 6 172 768 + 1;
  • 6 172 768 ÷ 2 = 3 086 384 + 0;
  • 3 086 384 ÷ 2 = 1 543 192 + 0;
  • 1 543 192 ÷ 2 = 771 596 + 0;
  • 771 596 ÷ 2 = 385 798 + 0;
  • 385 798 ÷ 2 = 192 899 + 0;
  • 192 899 ÷ 2 = 96 449 + 1;
  • 96 449 ÷ 2 = 48 224 + 1;
  • 48 224 ÷ 2 = 24 112 + 0;
  • 24 112 ÷ 2 = 12 056 + 0;
  • 12 056 ÷ 2 = 6 028 + 0;
  • 6 028 ÷ 2 = 3 014 + 0;
  • 3 014 ÷ 2 = 1 507 + 0;
  • 1 507 ÷ 2 = 753 + 1;
  • 753 ÷ 2 = 376 + 1;
  • 376 ÷ 2 = 188 + 0;
  • 188 ÷ 2 = 94 + 0;
  • 94 ÷ 2 = 47 + 0;
  • 47 ÷ 2 = 23 + 1;
  • 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 12 345 537(10), a positive integer number (with no sign),
converted from decimal system (from base 10)
and written as an unsigned binary (in base 2):

12 345 537(10) = 1011 1100 0110 0000 1100 0001(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)