Unsigned: Integer ↗ Binary: 4 293 918 716 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 4 293 918 716(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;
  • 4 293 918 716 ÷ 2 = 2 146 959 358 + 0;
  • 2 146 959 358 ÷ 2 = 1 073 479 679 + 0;
  • 1 073 479 679 ÷ 2 = 536 739 839 + 1;
  • 536 739 839 ÷ 2 = 268 369 919 + 1;
  • 268 369 919 ÷ 2 = 134 184 959 + 1;
  • 134 184 959 ÷ 2 = 67 092 479 + 1;
  • 67 092 479 ÷ 2 = 33 546 239 + 1;
  • 33 546 239 ÷ 2 = 16 773 119 + 1;
  • 16 773 119 ÷ 2 = 8 386 559 + 1;
  • 8 386 559 ÷ 2 = 4 193 279 + 1;
  • 4 193 279 ÷ 2 = 2 096 639 + 1;
  • 2 096 639 ÷ 2 = 1 048 319 + 1;
  • 1 048 319 ÷ 2 = 524 159 + 1;
  • 524 159 ÷ 2 = 262 079 + 1;
  • 262 079 ÷ 2 = 131 039 + 1;
  • 131 039 ÷ 2 = 65 519 + 1;
  • 65 519 ÷ 2 = 32 759 + 1;
  • 32 759 ÷ 2 = 16 379 + 1;
  • 16 379 ÷ 2 = 8 189 + 1;
  • 8 189 ÷ 2 = 4 094 + 1;
  • 4 094 ÷ 2 = 2 047 + 0;
  • 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 4 293 918 716(10), a positive integer number (with no sign),
converted from decimal system (from base 10)
and written as an unsigned binary (in base 2):

4 293 918 716(10) = 1111 1111 1110 1111 1111 1111 1111 1100(2)

Spaces were used to group digits: for binary, by 4, for decimal, by 3.

The latest positive (unsigned) integer numbers converted from decimal system (written in base ten) to unsigned binary (written in base two)

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)