Base Ten to Base Two: Unsigned Number 1 001 000 043 Converted and Written in Base Two. Natural Number (Positive Integer, No Sign) Converted From Decimal System to Binary Code

Base ten unsigned number 1 001 000 043(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;
  • 1 001 000 043 ÷ 2 = 500 500 021 + 1;
  • 500 500 021 ÷ 2 = 250 250 010 + 1;
  • 250 250 010 ÷ 2 = 125 125 005 + 0;
  • 125 125 005 ÷ 2 = 62 562 502 + 1;
  • 62 562 502 ÷ 2 = 31 281 251 + 0;
  • 31 281 251 ÷ 2 = 15 640 625 + 1;
  • 15 640 625 ÷ 2 = 7 820 312 + 1;
  • 7 820 312 ÷ 2 = 3 910 156 + 0;
  • 3 910 156 ÷ 2 = 1 955 078 + 0;
  • 1 955 078 ÷ 2 = 977 539 + 0;
  • 977 539 ÷ 2 = 488 769 + 1;
  • 488 769 ÷ 2 = 244 384 + 1;
  • 244 384 ÷ 2 = 122 192 + 0;
  • 122 192 ÷ 2 = 61 096 + 0;
  • 61 096 ÷ 2 = 30 548 + 0;
  • 30 548 ÷ 2 = 15 274 + 0;
  • 15 274 ÷ 2 = 7 637 + 0;
  • 7 637 ÷ 2 = 3 818 + 1;
  • 3 818 ÷ 2 = 1 909 + 0;
  • 1 909 ÷ 2 = 954 + 1;
  • 954 ÷ 2 = 477 + 0;
  • 477 ÷ 2 = 238 + 1;
  • 238 ÷ 2 = 119 + 0;
  • 119 ÷ 2 = 59 + 1;
  • 59 ÷ 2 = 29 + 1;
  • 29 ÷ 2 = 14 + 1;
  • 14 ÷ 2 = 7 + 0;
  • 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 1 001 000 043(10), a positive integer number (with no sign),
converted from decimal system (from base 10)
and written as an unsigned binary (in base 2):

1 001 000 043(10) = 11 1011 1010 1010 0000 1100 0110 1011(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)