Unsigned: Integer ↗ Binary: 8 589 766 748 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 8 589 766 748(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;
  • 8 589 766 748 ÷ 2 = 4 294 883 374 + 0;
  • 4 294 883 374 ÷ 2 = 2 147 441 687 + 0;
  • 2 147 441 687 ÷ 2 = 1 073 720 843 + 1;
  • 1 073 720 843 ÷ 2 = 536 860 421 + 1;
  • 536 860 421 ÷ 2 = 268 430 210 + 1;
  • 268 430 210 ÷ 2 = 134 215 105 + 0;
  • 134 215 105 ÷ 2 = 67 107 552 + 1;
  • 67 107 552 ÷ 2 = 33 553 776 + 0;
  • 33 553 776 ÷ 2 = 16 776 888 + 0;
  • 16 776 888 ÷ 2 = 8 388 444 + 0;
  • 8 388 444 ÷ 2 = 4 194 222 + 0;
  • 4 194 222 ÷ 2 = 2 097 111 + 0;
  • 2 097 111 ÷ 2 = 1 048 555 + 1;
  • 1 048 555 ÷ 2 = 524 277 + 1;
  • 524 277 ÷ 2 = 262 138 + 1;
  • 262 138 ÷ 2 = 131 069 + 0;
  • 131 069 ÷ 2 = 65 534 + 1;
  • 65 534 ÷ 2 = 32 767 + 0;
  • 32 767 ÷ 2 = 16 383 + 1;
  • 16 383 ÷ 2 = 8 191 + 1;
  • 8 191 ÷ 2 = 4 095 + 1;
  • 4 095 ÷ 2 = 2 047 + 1;
  • 2 047 ÷ 2 = 1 023 + 1;
  • 1 023 ÷ 2 = 511 + 1;
  • 511 ÷ 2 = 255 + 1;
  • 255 ÷ 2 = 127 + 1;
  • 127 ÷ 2 = 63 + 1;
  • 63 ÷ 2 = 31 + 1;
  • 31 ÷ 2 = 15 + 1;
  • 15 ÷ 2 = 7 + 1;
  • 7 ÷ 2 = 3 + 1;
  • 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 8 589 766 748(10), a positive integer number (with no sign),
converted from decimal system (from base 10)
and written as an unsigned binary (in base 2):

8 589 766 748(10) = 1 1111 1111 1111 1101 0111 0000 0101 1100(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 8 589 766 747 converted from decimal system (from base 10) and written as an unsigned binary (in base 2) = ?

» Unsigned (positive) integer number 8 589 766 749 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)