Unsigned: Integer ↗ Binary: 10 101 101 100 089 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 10 101 101 100 089(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;
  • 10 101 101 100 089 ÷ 2 = 5 050 550 550 044 + 1;
  • 5 050 550 550 044 ÷ 2 = 2 525 275 275 022 + 0;
  • 2 525 275 275 022 ÷ 2 = 1 262 637 637 511 + 0;
  • 1 262 637 637 511 ÷ 2 = 631 318 818 755 + 1;
  • 631 318 818 755 ÷ 2 = 315 659 409 377 + 1;
  • 315 659 409 377 ÷ 2 = 157 829 704 688 + 1;
  • 157 829 704 688 ÷ 2 = 78 914 852 344 + 0;
  • 78 914 852 344 ÷ 2 = 39 457 426 172 + 0;
  • 39 457 426 172 ÷ 2 = 19 728 713 086 + 0;
  • 19 728 713 086 ÷ 2 = 9 864 356 543 + 0;
  • 9 864 356 543 ÷ 2 = 4 932 178 271 + 1;
  • 4 932 178 271 ÷ 2 = 2 466 089 135 + 1;
  • 2 466 089 135 ÷ 2 = 1 233 044 567 + 1;
  • 1 233 044 567 ÷ 2 = 616 522 283 + 1;
  • 616 522 283 ÷ 2 = 308 261 141 + 1;
  • 308 261 141 ÷ 2 = 154 130 570 + 1;
  • 154 130 570 ÷ 2 = 77 065 285 + 0;
  • 77 065 285 ÷ 2 = 38 532 642 + 1;
  • 38 532 642 ÷ 2 = 19 266 321 + 0;
  • 19 266 321 ÷ 2 = 9 633 160 + 1;
  • 9 633 160 ÷ 2 = 4 816 580 + 0;
  • 4 816 580 ÷ 2 = 2 408 290 + 0;
  • 2 408 290 ÷ 2 = 1 204 145 + 0;
  • 1 204 145 ÷ 2 = 602 072 + 1;
  • 602 072 ÷ 2 = 301 036 + 0;
  • 301 036 ÷ 2 = 150 518 + 0;
  • 150 518 ÷ 2 = 75 259 + 0;
  • 75 259 ÷ 2 = 37 629 + 1;
  • 37 629 ÷ 2 = 18 814 + 1;
  • 18 814 ÷ 2 = 9 407 + 0;
  • 9 407 ÷ 2 = 4 703 + 1;
  • 4 703 ÷ 2 = 2 351 + 1;
  • 2 351 ÷ 2 = 1 175 + 1;
  • 1 175 ÷ 2 = 587 + 1;
  • 587 ÷ 2 = 293 + 1;
  • 293 ÷ 2 = 146 + 1;
  • 146 ÷ 2 = 73 + 0;
  • 73 ÷ 2 = 36 + 1;
  • 36 ÷ 2 = 18 + 0;
  • 18 ÷ 2 = 9 + 0;
  • 9 ÷ 2 = 4 + 1;
  • 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 10 101 101 100 089(10), a positive integer number (with no sign),
converted from decimal system (from base 10)
and written as an unsigned binary (in base 2):

10 101 101 100 089(10) = 1001 0010 1111 1101 1000 1000 1010 1111 1100 0011 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 10 101 101 100 088 converted from decimal system (from base 10) and written as an unsigned binary (in base 2) = ?

» Unsigned (positive) integer number 10 101 101 100 090 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)