Base ten decimal system unsigned (positive) integer number 11 111 111 111 converted to unsigned binary (base two)

How to convert an unsigned (positive) integer in decimal system (in base 10):
11 111 111 111(10)
to an unsigned binary (base 2)

1. Divide the number repeatedly by 2, keeping track of each remainder, until we get a quotient that is equal to zero:

  • division = quotient + remainder;
  • 11 111 111 111 ÷ 2 = 5 555 555 555 + 1;
  • 5 555 555 555 ÷ 2 = 2 777 777 777 + 1;
  • 2 777 777 777 ÷ 2 = 1 388 888 888 + 1;
  • 1 388 888 888 ÷ 2 = 694 444 444 + 0;
  • 694 444 444 ÷ 2 = 347 222 222 + 0;
  • 347 222 222 ÷ 2 = 173 611 111 + 0;
  • 173 611 111 ÷ 2 = 86 805 555 + 1;
  • 86 805 555 ÷ 2 = 43 402 777 + 1;
  • 43 402 777 ÷ 2 = 21 701 388 + 1;
  • 21 701 388 ÷ 2 = 10 850 694 + 0;
  • 10 850 694 ÷ 2 = 5 425 347 + 0;
  • 5 425 347 ÷ 2 = 2 712 673 + 1;
  • 2 712 673 ÷ 2 = 1 356 336 + 1;
  • 1 356 336 ÷ 2 = 678 168 + 0;
  • 678 168 ÷ 2 = 339 084 + 0;
  • 339 084 ÷ 2 = 169 542 + 0;
  • 169 542 ÷ 2 = 84 771 + 0;
  • 84 771 ÷ 2 = 42 385 + 1;
  • 42 385 ÷ 2 = 21 192 + 1;
  • 21 192 ÷ 2 = 10 596 + 0;
  • 10 596 ÷ 2 = 5 298 + 0;
  • 5 298 ÷ 2 = 2 649 + 0;
  • 2 649 ÷ 2 = 1 324 + 1;
  • 1 324 ÷ 2 = 662 + 0;
  • 662 ÷ 2 = 331 + 0;
  • 331 ÷ 2 = 165 + 1;
  • 165 ÷ 2 = 82 + 1;
  • 82 ÷ 2 = 41 + 0;
  • 41 ÷ 2 = 20 + 1;
  • 20 ÷ 2 = 10 + 0;
  • 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, by taking all the remainders starting from the bottom of the list constructed above:

11 111 111 111(10) = 10 1001 0110 0100 0110 0001 1001 1100 0111(2)

Conclusion:

Number 11 111 111 111(10), a positive integer (no sign), converted from decimal system (base 10) to an unsigned binary (base 2):


10 1001 0110 0100 0110 0001 1001 1100 0111(2)

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

Convert positive integer numbers (unsigned) from the decimal system (base ten) to binary (base two)

How to convert a base ten positive integer number to base two:

1) Divide the number repeatedly by 2, keeping track of each remainder, until we get a quotient that is ZERO;

2) Construct the base 2 representation by taking all the previously calculated remainders starting from the last remainder up to the first one, in that order.

Latest positive integer numbers (unsigned) converted from decimal (base ten) to unsigned binary (base two)

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)