Unsigned: Integer ↗ Binary: 1 071 225 241 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 1 071 225 241(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;
  • 1 071 225 241 ÷ 2 = 535 612 620 + 1;
  • 535 612 620 ÷ 2 = 267 806 310 + 0;
  • 267 806 310 ÷ 2 = 133 903 155 + 0;
  • 133 903 155 ÷ 2 = 66 951 577 + 1;
  • 66 951 577 ÷ 2 = 33 475 788 + 1;
  • 33 475 788 ÷ 2 = 16 737 894 + 0;
  • 16 737 894 ÷ 2 = 8 368 947 + 0;
  • 8 368 947 ÷ 2 = 4 184 473 + 1;
  • 4 184 473 ÷ 2 = 2 092 236 + 1;
  • 2 092 236 ÷ 2 = 1 046 118 + 0;
  • 1 046 118 ÷ 2 = 523 059 + 0;
  • 523 059 ÷ 2 = 261 529 + 1;
  • 261 529 ÷ 2 = 130 764 + 1;
  • 130 764 ÷ 2 = 65 382 + 0;
  • 65 382 ÷ 2 = 32 691 + 0;
  • 32 691 ÷ 2 = 16 345 + 1;
  • 16 345 ÷ 2 = 8 172 + 1;
  • 8 172 ÷ 2 = 4 086 + 0;
  • 4 086 ÷ 2 = 2 043 + 0;
  • 2 043 ÷ 2 = 1 021 + 1;
  • 1 021 ÷ 2 = 510 + 1;
  • 510 ÷ 2 = 255 + 0;
  • 255 ÷ 2 = 127 + 1;
  • 127 ÷ 2 = 63 + 1;
  • 63 ÷ 2 = 31 + 1;
  • 31 ÷ 2 = 15 + 1;
  • 15 ÷ 2 = 7 + 1;
  • 7 ÷ 2 = 3 + 1;
  • 3 ÷ 2 = 1 + 1;
  • 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 1 071 225 241(10), a positive integer number (with no sign),
converted from decimal system (from base 10)
and written as an unsigned binary (in base 2):

1 071 225 241(10) = 11 1111 1101 1001 1001 1001 1001 1001(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 1 071 225 240 converted from decimal system (from base 10) and written as an unsigned binary (in base 2) = ?

» Unsigned (positive) integer number 1 071 225 242 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)