Unsigned: Integer ↗ Binary: 3 187 174 379 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 3 187 174 379(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;
  • 3 187 174 379 ÷ 2 = 1 593 587 189 + 1;
  • 1 593 587 189 ÷ 2 = 796 793 594 + 1;
  • 796 793 594 ÷ 2 = 398 396 797 + 0;
  • 398 396 797 ÷ 2 = 199 198 398 + 1;
  • 199 198 398 ÷ 2 = 99 599 199 + 0;
  • 99 599 199 ÷ 2 = 49 799 599 + 1;
  • 49 799 599 ÷ 2 = 24 899 799 + 1;
  • 24 899 799 ÷ 2 = 12 449 899 + 1;
  • 12 449 899 ÷ 2 = 6 224 949 + 1;
  • 6 224 949 ÷ 2 = 3 112 474 + 1;
  • 3 112 474 ÷ 2 = 1 556 237 + 0;
  • 1 556 237 ÷ 2 = 778 118 + 1;
  • 778 118 ÷ 2 = 389 059 + 0;
  • 389 059 ÷ 2 = 194 529 + 1;
  • 194 529 ÷ 2 = 97 264 + 1;
  • 97 264 ÷ 2 = 48 632 + 0;
  • 48 632 ÷ 2 = 24 316 + 0;
  • 24 316 ÷ 2 = 12 158 + 0;
  • 12 158 ÷ 2 = 6 079 + 0;
  • 6 079 ÷ 2 = 3 039 + 1;
  • 3 039 ÷ 2 = 1 519 + 1;
  • 1 519 ÷ 2 = 759 + 1;
  • 759 ÷ 2 = 379 + 1;
  • 379 ÷ 2 = 189 + 1;
  • 189 ÷ 2 = 94 + 1;
  • 94 ÷ 2 = 47 + 0;
  • 47 ÷ 2 = 23 + 1;
  • 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 3 187 174 379(10), a positive integer number (with no sign),
converted from decimal system (from base 10)
and written as an unsigned binary (in base 2):

3 187 174 379(10) = 1011 1101 1111 1000 0110 1011 1110 1011(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 3 187 174 378 converted from decimal system (from base 10) and written as an unsigned binary (in base 2) = ?

» Unsigned (positive) integer number 3 187 174 380 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)