Base ten decimal system unsigned (positive) integer number 110 101 101 converted to unsigned binary (base two)

How to convert an unsigned (positive) integer in decimal system (in base 10):
110 101 101(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;
  • 110 101 101 ÷ 2 = 55 050 550 + 1;
  • 55 050 550 ÷ 2 = 27 525 275 + 0;
  • 27 525 275 ÷ 2 = 13 762 637 + 1;
  • 13 762 637 ÷ 2 = 6 881 318 + 1;
  • 6 881 318 ÷ 2 = 3 440 659 + 0;
  • 3 440 659 ÷ 2 = 1 720 329 + 1;
  • 1 720 329 ÷ 2 = 860 164 + 1;
  • 860 164 ÷ 2 = 430 082 + 0;
  • 430 082 ÷ 2 = 215 041 + 0;
  • 215 041 ÷ 2 = 107 520 + 1;
  • 107 520 ÷ 2 = 53 760 + 0;
  • 53 760 ÷ 2 = 26 880 + 0;
  • 26 880 ÷ 2 = 13 440 + 0;
  • 13 440 ÷ 2 = 6 720 + 0;
  • 6 720 ÷ 2 = 3 360 + 0;
  • 3 360 ÷ 2 = 1 680 + 0;
  • 1 680 ÷ 2 = 840 + 0;
  • 840 ÷ 2 = 420 + 0;
  • 420 ÷ 2 = 210 + 0;
  • 210 ÷ 2 = 105 + 0;
  • 105 ÷ 2 = 52 + 1;
  • 52 ÷ 2 = 26 + 0;
  • 26 ÷ 2 = 13 + 0;
  • 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 number, by taking all the remainders starting from the bottom of the list constructed above:

110 101 101(10) = 110 1001 0000 0000 0010 0110 1101(2)

Conclusion:

Number 110 101 101(10), a positive integer (no sign), converted from decimal system (base 10) to an unsigned binary (base 2):


110 1001 0000 0000 0010 0110 1101(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)