Unsigned: Integer ↗ Binary: 1 001 001 001 100 010 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 1 001 001 001 100 010(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;
  • 1 001 001 001 100 010 ÷ 2 = 500 500 500 550 005 + 0;
  • 500 500 500 550 005 ÷ 2 = 250 250 250 275 002 + 1;
  • 250 250 250 275 002 ÷ 2 = 125 125 125 137 501 + 0;
  • 125 125 125 137 501 ÷ 2 = 62 562 562 568 750 + 1;
  • 62 562 562 568 750 ÷ 2 = 31 281 281 284 375 + 0;
  • 31 281 281 284 375 ÷ 2 = 15 640 640 642 187 + 1;
  • 15 640 640 642 187 ÷ 2 = 7 820 320 321 093 + 1;
  • 7 820 320 321 093 ÷ 2 = 3 910 160 160 546 + 1;
  • 3 910 160 160 546 ÷ 2 = 1 955 080 080 273 + 0;
  • 1 955 080 080 273 ÷ 2 = 977 540 040 136 + 1;
  • 977 540 040 136 ÷ 2 = 488 770 020 068 + 0;
  • 488 770 020 068 ÷ 2 = 244 385 010 034 + 0;
  • 244 385 010 034 ÷ 2 = 122 192 505 017 + 0;
  • 122 192 505 017 ÷ 2 = 61 096 252 508 + 1;
  • 61 096 252 508 ÷ 2 = 30 548 126 254 + 0;
  • 30 548 126 254 ÷ 2 = 15 274 063 127 + 0;
  • 15 274 063 127 ÷ 2 = 7 637 031 563 + 1;
  • 7 637 031 563 ÷ 2 = 3 818 515 781 + 1;
  • 3 818 515 781 ÷ 2 = 1 909 257 890 + 1;
  • 1 909 257 890 ÷ 2 = 954 628 945 + 0;
  • 954 628 945 ÷ 2 = 477 314 472 + 1;
  • 477 314 472 ÷ 2 = 238 657 236 + 0;
  • 238 657 236 ÷ 2 = 119 328 618 + 0;
  • 119 328 618 ÷ 2 = 59 664 309 + 0;
  • 59 664 309 ÷ 2 = 29 832 154 + 1;
  • 29 832 154 ÷ 2 = 14 916 077 + 0;
  • 14 916 077 ÷ 2 = 7 458 038 + 1;
  • 7 458 038 ÷ 2 = 3 729 019 + 0;
  • 3 729 019 ÷ 2 = 1 864 509 + 1;
  • 1 864 509 ÷ 2 = 932 254 + 1;
  • 932 254 ÷ 2 = 466 127 + 0;
  • 466 127 ÷ 2 = 233 063 + 1;
  • 233 063 ÷ 2 = 116 531 + 1;
  • 116 531 ÷ 2 = 58 265 + 1;
  • 58 265 ÷ 2 = 29 132 + 1;
  • 29 132 ÷ 2 = 14 566 + 0;
  • 14 566 ÷ 2 = 7 283 + 0;
  • 7 283 ÷ 2 = 3 641 + 1;
  • 3 641 ÷ 2 = 1 820 + 1;
  • 1 820 ÷ 2 = 910 + 0;
  • 910 ÷ 2 = 455 + 0;
  • 455 ÷ 2 = 227 + 1;
  • 227 ÷ 2 = 113 + 1;
  • 113 ÷ 2 = 56 + 1;
  • 56 ÷ 2 = 28 + 0;
  • 28 ÷ 2 = 14 + 0;
  • 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 1 001 001 001 100 010(10), a positive integer number (with no sign),
converted from decimal system (from base 10)
and written as an unsigned binary (in base 2):

1 001 001 001 100 010(10) = 11 1000 1110 0110 0111 1011 0101 0001 0111 0010 0010 1110 1010(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 1 001 001 001 100 009 converted from decimal system (from base 10) and written as an unsigned binary (in base 2) = ?

» Unsigned (positive) integer number 1 001 001 001 100 011 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)