Unsigned: Integer ↗ Binary: 6 999 999 976 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 6 999 999 976(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;
  • 6 999 999 976 ÷ 2 = 3 499 999 988 + 0;
  • 3 499 999 988 ÷ 2 = 1 749 999 994 + 0;
  • 1 749 999 994 ÷ 2 = 874 999 997 + 0;
  • 874 999 997 ÷ 2 = 437 499 998 + 1;
  • 437 499 998 ÷ 2 = 218 749 999 + 0;
  • 218 749 999 ÷ 2 = 109 374 999 + 1;
  • 109 374 999 ÷ 2 = 54 687 499 + 1;
  • 54 687 499 ÷ 2 = 27 343 749 + 1;
  • 27 343 749 ÷ 2 = 13 671 874 + 1;
  • 13 671 874 ÷ 2 = 6 835 937 + 0;
  • 6 835 937 ÷ 2 = 3 417 968 + 1;
  • 3 417 968 ÷ 2 = 1 708 984 + 0;
  • 1 708 984 ÷ 2 = 854 492 + 0;
  • 854 492 ÷ 2 = 427 246 + 0;
  • 427 246 ÷ 2 = 213 623 + 0;
  • 213 623 ÷ 2 = 106 811 + 1;
  • 106 811 ÷ 2 = 53 405 + 1;
  • 53 405 ÷ 2 = 26 702 + 1;
  • 26 702 ÷ 2 = 13 351 + 0;
  • 13 351 ÷ 2 = 6 675 + 1;
  • 6 675 ÷ 2 = 3 337 + 1;
  • 3 337 ÷ 2 = 1 668 + 1;
  • 1 668 ÷ 2 = 834 + 0;
  • 834 ÷ 2 = 417 + 0;
  • 417 ÷ 2 = 208 + 1;
  • 208 ÷ 2 = 104 + 0;
  • 104 ÷ 2 = 52 + 0;
  • 52 ÷ 2 = 26 + 0;
  • 26 ÷ 2 = 13 + 0;
  • 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 number:

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


Number 6 999 999 976(10), a positive integer number (with no sign),
converted from decimal system (from base 10)
and written as an unsigned binary (in base 2):

6 999 999 976(10) = 1 1010 0001 0011 1011 1000 0101 1110 1000(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 6 999 999 975 converted from decimal system (from base 10) and written as an unsigned binary (in base 2) = ?

» Unsigned (positive) integer number 6 999 999 977 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)