Unsigned: Integer ↗ Binary: 1 001 001 001 065 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 1 001 001 001 065(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;
  • 1 001 001 001 065 ÷ 2 = 500 500 500 532 + 1;
  • 500 500 500 532 ÷ 2 = 250 250 250 266 + 0;
  • 250 250 250 266 ÷ 2 = 125 125 125 133 + 0;
  • 125 125 125 133 ÷ 2 = 62 562 562 566 + 1;
  • 62 562 562 566 ÷ 2 = 31 281 281 283 + 0;
  • 31 281 281 283 ÷ 2 = 15 640 640 641 + 1;
  • 15 640 640 641 ÷ 2 = 7 820 320 320 + 1;
  • 7 820 320 320 ÷ 2 = 3 910 160 160 + 0;
  • 3 910 160 160 ÷ 2 = 1 955 080 080 + 0;
  • 1 955 080 080 ÷ 2 = 977 540 040 + 0;
  • 977 540 040 ÷ 2 = 488 770 020 + 0;
  • 488 770 020 ÷ 2 = 244 385 010 + 0;
  • 244 385 010 ÷ 2 = 122 192 505 + 0;
  • 122 192 505 ÷ 2 = 61 096 252 + 1;
  • 61 096 252 ÷ 2 = 30 548 126 + 0;
  • 30 548 126 ÷ 2 = 15 274 063 + 0;
  • 15 274 063 ÷ 2 = 7 637 031 + 1;
  • 7 637 031 ÷ 2 = 3 818 515 + 1;
  • 3 818 515 ÷ 2 = 1 909 257 + 1;
  • 1 909 257 ÷ 2 = 954 628 + 1;
  • 954 628 ÷ 2 = 477 314 + 0;
  • 477 314 ÷ 2 = 238 657 + 0;
  • 238 657 ÷ 2 = 119 328 + 1;
  • 119 328 ÷ 2 = 59 664 + 0;
  • 59 664 ÷ 2 = 29 832 + 0;
  • 29 832 ÷ 2 = 14 916 + 0;
  • 14 916 ÷ 2 = 7 458 + 0;
  • 7 458 ÷ 2 = 3 729 + 0;
  • 3 729 ÷ 2 = 1 864 + 1;
  • 1 864 ÷ 2 = 932 + 0;
  • 932 ÷ 2 = 466 + 0;
  • 466 ÷ 2 = 233 + 0;
  • 233 ÷ 2 = 116 + 1;
  • 116 ÷ 2 = 58 + 0;
  • 58 ÷ 2 = 29 + 0;
  • 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 1 001 001 001 065(10), a positive integer number (with no sign),
converted from decimal system (from base 10)
and written as an unsigned binary (in base 2):

1 001 001 001 065(10) = 1110 1001 0001 0000 0100 1111 0010 0000 0110 1001(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 1 001 001 001 064 converted from decimal system (from base 10) and written as an unsigned binary (in base 2) = ?

» Unsigned (positive) integer number 1 001 001 001 066 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)