Unsigned: Integer ↗ Binary: 11 000 001 010 100 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 11 000 001 010 100(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;
  • 11 000 001 010 100 ÷ 2 = 5 500 000 505 050 + 0;
  • 5 500 000 505 050 ÷ 2 = 2 750 000 252 525 + 0;
  • 2 750 000 252 525 ÷ 2 = 1 375 000 126 262 + 1;
  • 1 375 000 126 262 ÷ 2 = 687 500 063 131 + 0;
  • 687 500 063 131 ÷ 2 = 343 750 031 565 + 1;
  • 343 750 031 565 ÷ 2 = 171 875 015 782 + 1;
  • 171 875 015 782 ÷ 2 = 85 937 507 891 + 0;
  • 85 937 507 891 ÷ 2 = 42 968 753 945 + 1;
  • 42 968 753 945 ÷ 2 = 21 484 376 972 + 1;
  • 21 484 376 972 ÷ 2 = 10 742 188 486 + 0;
  • 10 742 188 486 ÷ 2 = 5 371 094 243 + 0;
  • 5 371 094 243 ÷ 2 = 2 685 547 121 + 1;
  • 2 685 547 121 ÷ 2 = 1 342 773 560 + 1;
  • 1 342 773 560 ÷ 2 = 671 386 780 + 0;
  • 671 386 780 ÷ 2 = 335 693 390 + 0;
  • 335 693 390 ÷ 2 = 167 846 695 + 0;
  • 167 846 695 ÷ 2 = 83 923 347 + 1;
  • 83 923 347 ÷ 2 = 41 961 673 + 1;
  • 41 961 673 ÷ 2 = 20 980 836 + 1;
  • 20 980 836 ÷ 2 = 10 490 418 + 0;
  • 10 490 418 ÷ 2 = 5 245 209 + 0;
  • 5 245 209 ÷ 2 = 2 622 604 + 1;
  • 2 622 604 ÷ 2 = 1 311 302 + 0;
  • 1 311 302 ÷ 2 = 655 651 + 0;
  • 655 651 ÷ 2 = 327 825 + 1;
  • 327 825 ÷ 2 = 163 912 + 1;
  • 163 912 ÷ 2 = 81 956 + 0;
  • 81 956 ÷ 2 = 40 978 + 0;
  • 40 978 ÷ 2 = 20 489 + 0;
  • 20 489 ÷ 2 = 10 244 + 1;
  • 10 244 ÷ 2 = 5 122 + 0;
  • 5 122 ÷ 2 = 2 561 + 0;
  • 2 561 ÷ 2 = 1 280 + 1;
  • 1 280 ÷ 2 = 640 + 0;
  • 640 ÷ 2 = 320 + 0;
  • 320 ÷ 2 = 160 + 0;
  • 160 ÷ 2 = 80 + 0;
  • 80 ÷ 2 = 40 + 0;
  • 40 ÷ 2 = 20 + 0;
  • 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:

Take all the remainders starting from the bottom of the list constructed above.


Number 11 000 001 010 100(10), a positive integer number (with no sign),
converted from decimal system (from base 10)
and written as an unsigned binary (in base 2):

11 000 001 010 100(10) = 1010 0000 0001 0010 0011 0010 0111 0001 1001 1011 0100(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 11 000 001 010 099 converted from decimal system (from base 10) and written as an unsigned binary (in base 2) = ?

» Unsigned (positive) integer number 11 000 001 010 101 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)