Unsigned: Integer ↗ Binary: 100 000 000 000 069 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 100 000 000 000 069(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;
  • 100 000 000 000 069 ÷ 2 = 50 000 000 000 034 + 1;
  • 50 000 000 000 034 ÷ 2 = 25 000 000 000 017 + 0;
  • 25 000 000 000 017 ÷ 2 = 12 500 000 000 008 + 1;
  • 12 500 000 000 008 ÷ 2 = 6 250 000 000 004 + 0;
  • 6 250 000 000 004 ÷ 2 = 3 125 000 000 002 + 0;
  • 3 125 000 000 002 ÷ 2 = 1 562 500 000 001 + 0;
  • 1 562 500 000 001 ÷ 2 = 781 250 000 000 + 1;
  • 781 250 000 000 ÷ 2 = 390 625 000 000 + 0;
  • 390 625 000 000 ÷ 2 = 195 312 500 000 + 0;
  • 195 312 500 000 ÷ 2 = 97 656 250 000 + 0;
  • 97 656 250 000 ÷ 2 = 48 828 125 000 + 0;
  • 48 828 125 000 ÷ 2 = 24 414 062 500 + 0;
  • 24 414 062 500 ÷ 2 = 12 207 031 250 + 0;
  • 12 207 031 250 ÷ 2 = 6 103 515 625 + 0;
  • 6 103 515 625 ÷ 2 = 3 051 757 812 + 1;
  • 3 051 757 812 ÷ 2 = 1 525 878 906 + 0;
  • 1 525 878 906 ÷ 2 = 762 939 453 + 0;
  • 762 939 453 ÷ 2 = 381 469 726 + 1;
  • 381 469 726 ÷ 2 = 190 734 863 + 0;
  • 190 734 863 ÷ 2 = 95 367 431 + 1;
  • 95 367 431 ÷ 2 = 47 683 715 + 1;
  • 47 683 715 ÷ 2 = 23 841 857 + 1;
  • 23 841 857 ÷ 2 = 11 920 928 + 1;
  • 11 920 928 ÷ 2 = 5 960 464 + 0;
  • 5 960 464 ÷ 2 = 2 980 232 + 0;
  • 2 980 232 ÷ 2 = 1 490 116 + 0;
  • 1 490 116 ÷ 2 = 745 058 + 0;
  • 745 058 ÷ 2 = 372 529 + 0;
  • 372 529 ÷ 2 = 186 264 + 1;
  • 186 264 ÷ 2 = 93 132 + 0;
  • 93 132 ÷ 2 = 46 566 + 0;
  • 46 566 ÷ 2 = 23 283 + 0;
  • 23 283 ÷ 2 = 11 641 + 1;
  • 11 641 ÷ 2 = 5 820 + 1;
  • 5 820 ÷ 2 = 2 910 + 0;
  • 2 910 ÷ 2 = 1 455 + 0;
  • 1 455 ÷ 2 = 727 + 1;
  • 727 ÷ 2 = 363 + 1;
  • 363 ÷ 2 = 181 + 1;
  • 181 ÷ 2 = 90 + 1;
  • 90 ÷ 2 = 45 + 0;
  • 45 ÷ 2 = 22 + 1;
  • 22 ÷ 2 = 11 + 0;
  • 11 ÷ 2 = 5 + 1;
  • 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 100 000 000 000 069(10), a positive integer number (with no sign),
converted from decimal system (from base 10)
and written as an unsigned binary (in base 2):

100 000 000 000 069(10) = 101 1010 1111 0011 0001 0000 0111 1010 0100 0000 0100 0101(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 100 000 000 000 068 converted from decimal system (from base 10) and written as an unsigned binary (in base 2) = ?

» Unsigned (positive) integer number 100 000 000 000 070 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)