Unsigned: Integer ↗ Binary: 110 010 001 002 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 110 010 001 002(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;
  • 110 010 001 002 ÷ 2 = 55 005 000 501 + 0;
  • 55 005 000 501 ÷ 2 = 27 502 500 250 + 1;
  • 27 502 500 250 ÷ 2 = 13 751 250 125 + 0;
  • 13 751 250 125 ÷ 2 = 6 875 625 062 + 1;
  • 6 875 625 062 ÷ 2 = 3 437 812 531 + 0;
  • 3 437 812 531 ÷ 2 = 1 718 906 265 + 1;
  • 1 718 906 265 ÷ 2 = 859 453 132 + 1;
  • 859 453 132 ÷ 2 = 429 726 566 + 0;
  • 429 726 566 ÷ 2 = 214 863 283 + 0;
  • 214 863 283 ÷ 2 = 107 431 641 + 1;
  • 107 431 641 ÷ 2 = 53 715 820 + 1;
  • 53 715 820 ÷ 2 = 26 857 910 + 0;
  • 26 857 910 ÷ 2 = 13 428 955 + 0;
  • 13 428 955 ÷ 2 = 6 714 477 + 1;
  • 6 714 477 ÷ 2 = 3 357 238 + 1;
  • 3 357 238 ÷ 2 = 1 678 619 + 0;
  • 1 678 619 ÷ 2 = 839 309 + 1;
  • 839 309 ÷ 2 = 419 654 + 1;
  • 419 654 ÷ 2 = 209 827 + 0;
  • 209 827 ÷ 2 = 104 913 + 1;
  • 104 913 ÷ 2 = 52 456 + 1;
  • 52 456 ÷ 2 = 26 228 + 0;
  • 26 228 ÷ 2 = 13 114 + 0;
  • 13 114 ÷ 2 = 6 557 + 0;
  • 6 557 ÷ 2 = 3 278 + 1;
  • 3 278 ÷ 2 = 1 639 + 0;
  • 1 639 ÷ 2 = 819 + 1;
  • 819 ÷ 2 = 409 + 1;
  • 409 ÷ 2 = 204 + 1;
  • 204 ÷ 2 = 102 + 0;
  • 102 ÷ 2 = 51 + 0;
  • 51 ÷ 2 = 25 + 1;
  • 25 ÷ 2 = 12 + 1;
  • 12 ÷ 2 = 6 + 0;
  • 6 ÷ 2 = 3 + 0;
  • 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 110 010 001 002(10), a positive integer number (with no sign),
converted from decimal system (from base 10)
and written as an unsigned binary (in base 2):

110 010 001 002(10) = 1 1001 1001 1101 0001 1011 0110 0110 0110 1010(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 110 010 001 001 converted from decimal system (from base 10) and written as an unsigned binary (in base 2) = ?

» Unsigned (positive) integer number 110 010 001 003 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)