Base Ten to Base Two: Unsigned Number 2 147 516 363 Converted and Written in Base Two. Natural Number (Positive Integer, No Sign) Converted From Decimal System to Binary Code

Base ten unsigned number 2 147 516 363(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;
  • 2 147 516 363 ÷ 2 = 1 073 758 181 + 1;
  • 1 073 758 181 ÷ 2 = 536 879 090 + 1;
  • 536 879 090 ÷ 2 = 268 439 545 + 0;
  • 268 439 545 ÷ 2 = 134 219 772 + 1;
  • 134 219 772 ÷ 2 = 67 109 886 + 0;
  • 67 109 886 ÷ 2 = 33 554 943 + 0;
  • 33 554 943 ÷ 2 = 16 777 471 + 1;
  • 16 777 471 ÷ 2 = 8 388 735 + 1;
  • 8 388 735 ÷ 2 = 4 194 367 + 1;
  • 4 194 367 ÷ 2 = 2 097 183 + 1;
  • 2 097 183 ÷ 2 = 1 048 591 + 1;
  • 1 048 591 ÷ 2 = 524 295 + 1;
  • 524 295 ÷ 2 = 262 147 + 1;
  • 262 147 ÷ 2 = 131 073 + 1;
  • 131 073 ÷ 2 = 65 536 + 1;
  • 65 536 ÷ 2 = 32 768 + 0;
  • 32 768 ÷ 2 = 16 384 + 0;
  • 16 384 ÷ 2 = 8 192 + 0;
  • 8 192 ÷ 2 = 4 096 + 0;
  • 4 096 ÷ 2 = 2 048 + 0;
  • 2 048 ÷ 2 = 1 024 + 0;
  • 1 024 ÷ 2 = 512 + 0;
  • 512 ÷ 2 = 256 + 0;
  • 256 ÷ 2 = 128 + 0;
  • 128 ÷ 2 = 64 + 0;
  • 64 ÷ 2 = 32 + 0;
  • 32 ÷ 2 = 16 + 0;
  • 16 ÷ 2 = 8 + 0;
  • 8 ÷ 2 = 4 + 0;
  • 4 ÷ 2 = 2 + 0;
  • 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 2 147 516 363(10), a positive integer number (with no sign),
converted from decimal system (from base 10)
and written as an unsigned binary (in base 2):

2 147 516 363(10) = 1000 0000 0000 0000 0111 1111 1100 1011(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)