Base Ten to Base Two: Unsigned Number 1 402 598 538 Converted and Written in Base Two. Natural Number (Positive Integer, No Sign) Converted From Decimal System to Binary Code

Base ten unsigned number 1 402 598 538(10) converted and written as a base two binary code

1. Divide the number repeatedly by 2:

Keep track of each remainder.

Stop when getting a quotient that is equal to zero.


  • division = quotient + remainder;
  • 1 402 598 538 ÷ 2 = 701 299 269 + 0;
  • 701 299 269 ÷ 2 = 350 649 634 + 1;
  • 350 649 634 ÷ 2 = 175 324 817 + 0;
  • 175 324 817 ÷ 2 = 87 662 408 + 1;
  • 87 662 408 ÷ 2 = 43 831 204 + 0;
  • 43 831 204 ÷ 2 = 21 915 602 + 0;
  • 21 915 602 ÷ 2 = 10 957 801 + 0;
  • 10 957 801 ÷ 2 = 5 478 900 + 1;
  • 5 478 900 ÷ 2 = 2 739 450 + 0;
  • 2 739 450 ÷ 2 = 1 369 725 + 0;
  • 1 369 725 ÷ 2 = 684 862 + 1;
  • 684 862 ÷ 2 = 342 431 + 0;
  • 342 431 ÷ 2 = 171 215 + 1;
  • 171 215 ÷ 2 = 85 607 + 1;
  • 85 607 ÷ 2 = 42 803 + 1;
  • 42 803 ÷ 2 = 21 401 + 1;
  • 21 401 ÷ 2 = 10 700 + 1;
  • 10 700 ÷ 2 = 5 350 + 0;
  • 5 350 ÷ 2 = 2 675 + 0;
  • 2 675 ÷ 2 = 1 337 + 1;
  • 1 337 ÷ 2 = 668 + 1;
  • 668 ÷ 2 = 334 + 0;
  • 334 ÷ 2 = 167 + 0;
  • 167 ÷ 2 = 83 + 1;
  • 83 ÷ 2 = 41 + 1;
  • 41 ÷ 2 = 20 + 1;
  • 20 ÷ 2 = 10 + 0;
  • 10 ÷ 2 = 5 + 0;
  • 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 1 402 598 538(10), a positive integer number (with no sign),
converted from decimal system (from base 10)
and written as an unsigned binary (in base 2):

1 402 598 538(10) = 101 0011 1001 1001 1111 0100 1000 1010(2)

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

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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)