Unsigned: Integer ↗ Binary: 12 586 269 026 Convert the Positive Integer (Whole Number) From Base Ten (10) To Base Two (2), Conversion and Writing of Decimal System Number as Unsigned Binary Code

Unsigned (positive) integer number 12 586 269 026(10)
converted and written as an unsigned binary (base 2) = ?

1. Divide the number repeatedly by 2:

Keep track of each remainder.

We stop when we get a quotient that is equal to zero.

  • division = quotient + remainder;
  • 12 586 269 026 ÷ 2 = 6 293 134 513 + 0;
  • 6 293 134 513 ÷ 2 = 3 146 567 256 + 1;
  • 3 146 567 256 ÷ 2 = 1 573 283 628 + 0;
  • 1 573 283 628 ÷ 2 = 786 641 814 + 0;
  • 786 641 814 ÷ 2 = 393 320 907 + 0;
  • 393 320 907 ÷ 2 = 196 660 453 + 1;
  • 196 660 453 ÷ 2 = 98 330 226 + 1;
  • 98 330 226 ÷ 2 = 49 165 113 + 0;
  • 49 165 113 ÷ 2 = 24 582 556 + 1;
  • 24 582 556 ÷ 2 = 12 291 278 + 0;
  • 12 291 278 ÷ 2 = 6 145 639 + 0;
  • 6 145 639 ÷ 2 = 3 072 819 + 1;
  • 3 072 819 ÷ 2 = 1 536 409 + 1;
  • 1 536 409 ÷ 2 = 768 204 + 1;
  • 768 204 ÷ 2 = 384 102 + 0;
  • 384 102 ÷ 2 = 192 051 + 0;
  • 192 051 ÷ 2 = 96 025 + 1;
  • 96 025 ÷ 2 = 48 012 + 1;
  • 48 012 ÷ 2 = 24 006 + 0;
  • 24 006 ÷ 2 = 12 003 + 0;
  • 12 003 ÷ 2 = 6 001 + 1;
  • 6 001 ÷ 2 = 3 000 + 1;
  • 3 000 ÷ 2 = 1 500 + 0;
  • 1 500 ÷ 2 = 750 + 0;
  • 750 ÷ 2 = 375 + 0;
  • 375 ÷ 2 = 187 + 1;
  • 187 ÷ 2 = 93 + 1;
  • 93 ÷ 2 = 46 + 1;
  • 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 12 586 269 026(10), a positive integer number (with no sign),
converted from decimal system (from base 10)
and written as an unsigned binary (in base 2):

12 586 269 026(10) = 10 1110 1110 0011 0011 0011 1001 0110 0010(2)

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

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All the decimal system (written in base ten) positive integers (with no sign) converted to unsigned binary (in base 2)

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)