Unsigned: Integer ↗ Binary: 1 001 011 001 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 1 001 011 001(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;
  • 1 001 011 001 ÷ 2 = 500 505 500 + 1;
  • 500 505 500 ÷ 2 = 250 252 750 + 0;
  • 250 252 750 ÷ 2 = 125 126 375 + 0;
  • 125 126 375 ÷ 2 = 62 563 187 + 1;
  • 62 563 187 ÷ 2 = 31 281 593 + 1;
  • 31 281 593 ÷ 2 = 15 640 796 + 1;
  • 15 640 796 ÷ 2 = 7 820 398 + 0;
  • 7 820 398 ÷ 2 = 3 910 199 + 0;
  • 3 910 199 ÷ 2 = 1 955 099 + 1;
  • 1 955 099 ÷ 2 = 977 549 + 1;
  • 977 549 ÷ 2 = 488 774 + 1;
  • 488 774 ÷ 2 = 244 387 + 0;
  • 244 387 ÷ 2 = 122 193 + 1;
  • 122 193 ÷ 2 = 61 096 + 1;
  • 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 1 001 011 001(10), a positive integer number (with no sign),
converted from decimal system (from base 10)
and written as an unsigned binary (in base 2):

1 001 011 001(10) = 11 1011 1010 1010 0011 0111 0011 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 1 001 011 000 converted from decimal system (from base 10) and written as an unsigned binary (in base 2) = ?

» Unsigned (positive) integer number 1 001 011 002 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)