Unsigned: Integer ↗ Binary: 1 100 001 105 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 1 100 001 105(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;
  • 1 100 001 105 ÷ 2 = 550 000 552 + 1;
  • 550 000 552 ÷ 2 = 275 000 276 + 0;
  • 275 000 276 ÷ 2 = 137 500 138 + 0;
  • 137 500 138 ÷ 2 = 68 750 069 + 0;
  • 68 750 069 ÷ 2 = 34 375 034 + 1;
  • 34 375 034 ÷ 2 = 17 187 517 + 0;
  • 17 187 517 ÷ 2 = 8 593 758 + 1;
  • 8 593 758 ÷ 2 = 4 296 879 + 0;
  • 4 296 879 ÷ 2 = 2 148 439 + 1;
  • 2 148 439 ÷ 2 = 1 074 219 + 1;
  • 1 074 219 ÷ 2 = 537 109 + 1;
  • 537 109 ÷ 2 = 268 554 + 1;
  • 268 554 ÷ 2 = 134 277 + 0;
  • 134 277 ÷ 2 = 67 138 + 1;
  • 67 138 ÷ 2 = 33 569 + 0;
  • 33 569 ÷ 2 = 16 784 + 1;
  • 16 784 ÷ 2 = 8 392 + 0;
  • 8 392 ÷ 2 = 4 196 + 0;
  • 4 196 ÷ 2 = 2 098 + 0;
  • 2 098 ÷ 2 = 1 049 + 0;
  • 1 049 ÷ 2 = 524 + 1;
  • 524 ÷ 2 = 262 + 0;
  • 262 ÷ 2 = 131 + 0;
  • 131 ÷ 2 = 65 + 1;
  • 65 ÷ 2 = 32 + 1;
  • 32 ÷ 2 = 16 + 0;
  • 16 ÷ 2 = 8 + 0;
  • 8 ÷ 2 = 4 + 0;
  • 4 ÷ 2 = 2 + 0;
  • 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 1 100 001 105(10), a positive integer number (with no sign),
converted from decimal system (from base 10)
and written as an unsigned binary (in base 2):

1 100 001 105(10) = 100 0001 1001 0000 1010 1111 0101 0001(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 1 100 001 104 converted from decimal system (from base 10) and written as an unsigned binary (in base 2) = ?

» Unsigned (positive) integer number 1 100 001 106 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)