Unsigned: Integer ↗ Binary: 3 455 645 637 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 3 455 645 637(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;
  • 3 455 645 637 ÷ 2 = 1 727 822 818 + 1;
  • 1 727 822 818 ÷ 2 = 863 911 409 + 0;
  • 863 911 409 ÷ 2 = 431 955 704 + 1;
  • 431 955 704 ÷ 2 = 215 977 852 + 0;
  • 215 977 852 ÷ 2 = 107 988 926 + 0;
  • 107 988 926 ÷ 2 = 53 994 463 + 0;
  • 53 994 463 ÷ 2 = 26 997 231 + 1;
  • 26 997 231 ÷ 2 = 13 498 615 + 1;
  • 13 498 615 ÷ 2 = 6 749 307 + 1;
  • 6 749 307 ÷ 2 = 3 374 653 + 1;
  • 3 374 653 ÷ 2 = 1 687 326 + 1;
  • 1 687 326 ÷ 2 = 843 663 + 0;
  • 843 663 ÷ 2 = 421 831 + 1;
  • 421 831 ÷ 2 = 210 915 + 1;
  • 210 915 ÷ 2 = 105 457 + 1;
  • 105 457 ÷ 2 = 52 728 + 1;
  • 52 728 ÷ 2 = 26 364 + 0;
  • 26 364 ÷ 2 = 13 182 + 0;
  • 13 182 ÷ 2 = 6 591 + 0;
  • 6 591 ÷ 2 = 3 295 + 1;
  • 3 295 ÷ 2 = 1 647 + 1;
  • 1 647 ÷ 2 = 823 + 1;
  • 823 ÷ 2 = 411 + 1;
  • 411 ÷ 2 = 205 + 1;
  • 205 ÷ 2 = 102 + 1;
  • 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 3 455 645 637(10), a positive integer number (with no sign),
converted from decimal system (from base 10)
and written as an unsigned binary (in base 2):

3 455 645 637(10) = 1100 1101 1111 1000 1111 0111 1100 0101(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 3 455 645 636 converted from decimal system (from base 10) and written as an unsigned binary (in base 2) = ?

» Unsigned (positive) integer number 3 455 645 638 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)