Unsigned: Integer ↗ Binary: 4 645 678 344 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 4 645 678 344(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;
  • 4 645 678 344 ÷ 2 = 2 322 839 172 + 0;
  • 2 322 839 172 ÷ 2 = 1 161 419 586 + 0;
  • 1 161 419 586 ÷ 2 = 580 709 793 + 0;
  • 580 709 793 ÷ 2 = 290 354 896 + 1;
  • 290 354 896 ÷ 2 = 145 177 448 + 0;
  • 145 177 448 ÷ 2 = 72 588 724 + 0;
  • 72 588 724 ÷ 2 = 36 294 362 + 0;
  • 36 294 362 ÷ 2 = 18 147 181 + 0;
  • 18 147 181 ÷ 2 = 9 073 590 + 1;
  • 9 073 590 ÷ 2 = 4 536 795 + 0;
  • 4 536 795 ÷ 2 = 2 268 397 + 1;
  • 2 268 397 ÷ 2 = 1 134 198 + 1;
  • 1 134 198 ÷ 2 = 567 099 + 0;
  • 567 099 ÷ 2 = 283 549 + 1;
  • 283 549 ÷ 2 = 141 774 + 1;
  • 141 774 ÷ 2 = 70 887 + 0;
  • 70 887 ÷ 2 = 35 443 + 1;
  • 35 443 ÷ 2 = 17 721 + 1;
  • 17 721 ÷ 2 = 8 860 + 1;
  • 8 860 ÷ 2 = 4 430 + 0;
  • 4 430 ÷ 2 = 2 215 + 0;
  • 2 215 ÷ 2 = 1 107 + 1;
  • 1 107 ÷ 2 = 553 + 1;
  • 553 ÷ 2 = 276 + 1;
  • 276 ÷ 2 = 138 + 0;
  • 138 ÷ 2 = 69 + 0;
  • 69 ÷ 2 = 34 + 1;
  • 34 ÷ 2 = 17 + 0;
  • 17 ÷ 2 = 8 + 1;
  • 8 ÷ 2 = 4 + 0;
  • 4 ÷ 2 = 2 + 0;
  • 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 4 645 678 344(10), a positive integer number (with no sign),
converted from decimal system (from base 10)
and written as an unsigned binary (in base 2):

4 645 678 344(10) = 1 0001 0100 1110 0111 0110 1101 0000 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 4 645 678 343 converted from decimal system (from base 10) and written as an unsigned binary (in base 2) = ?

» Unsigned (positive) integer number 4 645 678 345 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)