Unsigned: Integer ↗ Binary: 268 502 222 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 268 502 222(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;
  • 268 502 222 ÷ 2 = 134 251 111 + 0;
  • 134 251 111 ÷ 2 = 67 125 555 + 1;
  • 67 125 555 ÷ 2 = 33 562 777 + 1;
  • 33 562 777 ÷ 2 = 16 781 388 + 1;
  • 16 781 388 ÷ 2 = 8 390 694 + 0;
  • 8 390 694 ÷ 2 = 4 195 347 + 0;
  • 4 195 347 ÷ 2 = 2 097 673 + 1;
  • 2 097 673 ÷ 2 = 1 048 836 + 1;
  • 1 048 836 ÷ 2 = 524 418 + 0;
  • 524 418 ÷ 2 = 262 209 + 0;
  • 262 209 ÷ 2 = 131 104 + 1;
  • 131 104 ÷ 2 = 65 552 + 0;
  • 65 552 ÷ 2 = 32 776 + 0;
  • 32 776 ÷ 2 = 16 388 + 0;
  • 16 388 ÷ 2 = 8 194 + 0;
  • 8 194 ÷ 2 = 4 097 + 0;
  • 4 097 ÷ 2 = 2 048 + 1;
  • 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 268 502 222(10), a positive integer number (with no sign),
converted from decimal system (from base 10)
and written as an unsigned binary (in base 2):

268 502 222(10) = 1 0000 0000 0001 0000 0100 1100 1110(2)

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

More operations on unsigned integer numbers:

» Unsigned (positive) integer number 268 502 221 converted from decimal system (from base 10) and written as an unsigned binary (in base 2) = ?

» Unsigned (positive) integer number 268 502 223 converted from decimal system (from base 10) and written as an unsigned binary (in base 2) = ?

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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)