Unsigned: Integer ↗ Binary: 200 110 010 313 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 200 110 010 313(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;
  • 200 110 010 313 ÷ 2 = 100 055 005 156 + 1;
  • 100 055 005 156 ÷ 2 = 50 027 502 578 + 0;
  • 50 027 502 578 ÷ 2 = 25 013 751 289 + 0;
  • 25 013 751 289 ÷ 2 = 12 506 875 644 + 1;
  • 12 506 875 644 ÷ 2 = 6 253 437 822 + 0;
  • 6 253 437 822 ÷ 2 = 3 126 718 911 + 0;
  • 3 126 718 911 ÷ 2 = 1 563 359 455 + 1;
  • 1 563 359 455 ÷ 2 = 781 679 727 + 1;
  • 781 679 727 ÷ 2 = 390 839 863 + 1;
  • 390 839 863 ÷ 2 = 195 419 931 + 1;
  • 195 419 931 ÷ 2 = 97 709 965 + 1;
  • 97 709 965 ÷ 2 = 48 854 982 + 1;
  • 48 854 982 ÷ 2 = 24 427 491 + 0;
  • 24 427 491 ÷ 2 = 12 213 745 + 1;
  • 12 213 745 ÷ 2 = 6 106 872 + 1;
  • 6 106 872 ÷ 2 = 3 053 436 + 0;
  • 3 053 436 ÷ 2 = 1 526 718 + 0;
  • 1 526 718 ÷ 2 = 763 359 + 0;
  • 763 359 ÷ 2 = 381 679 + 1;
  • 381 679 ÷ 2 = 190 839 + 1;
  • 190 839 ÷ 2 = 95 419 + 1;
  • 95 419 ÷ 2 = 47 709 + 1;
  • 47 709 ÷ 2 = 23 854 + 1;
  • 23 854 ÷ 2 = 11 927 + 0;
  • 11 927 ÷ 2 = 5 963 + 1;
  • 5 963 ÷ 2 = 2 981 + 1;
  • 2 981 ÷ 2 = 1 490 + 1;
  • 1 490 ÷ 2 = 745 + 0;
  • 745 ÷ 2 = 372 + 1;
  • 372 ÷ 2 = 186 + 0;
  • 186 ÷ 2 = 93 + 0;
  • 93 ÷ 2 = 46 + 1;
  • 46 ÷ 2 = 23 + 0;
  • 23 ÷ 2 = 11 + 1;
  • 11 ÷ 2 = 5 + 1;
  • 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 200 110 010 313(10), a positive integer number (with no sign),
converted from decimal system (from base 10)
and written as an unsigned binary (in base 2):

200 110 010 313(10) = 10 1110 1001 0111 0111 1100 0110 1111 1100 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 200 110 010 312 converted from decimal system (from base 10) and written as an unsigned binary (in base 2) = ?

» Unsigned (positive) integer number 200 110 010 314 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)