Unsigned: Integer ↗ Binary: 37 834 377 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 37 834 377(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;
  • 37 834 377 ÷ 2 = 18 917 188 + 1;
  • 18 917 188 ÷ 2 = 9 458 594 + 0;
  • 9 458 594 ÷ 2 = 4 729 297 + 0;
  • 4 729 297 ÷ 2 = 2 364 648 + 1;
  • 2 364 648 ÷ 2 = 1 182 324 + 0;
  • 1 182 324 ÷ 2 = 591 162 + 0;
  • 591 162 ÷ 2 = 295 581 + 0;
  • 295 581 ÷ 2 = 147 790 + 1;
  • 147 790 ÷ 2 = 73 895 + 0;
  • 73 895 ÷ 2 = 36 947 + 1;
  • 36 947 ÷ 2 = 18 473 + 1;
  • 18 473 ÷ 2 = 9 236 + 1;
  • 9 236 ÷ 2 = 4 618 + 0;
  • 4 618 ÷ 2 = 2 309 + 0;
  • 2 309 ÷ 2 = 1 154 + 1;
  • 1 154 ÷ 2 = 577 + 0;
  • 577 ÷ 2 = 288 + 1;
  • 288 ÷ 2 = 144 + 0;
  • 144 ÷ 2 = 72 + 0;
  • 72 ÷ 2 = 36 + 0;
  • 36 ÷ 2 = 18 + 0;
  • 18 ÷ 2 = 9 + 0;
  • 9 ÷ 2 = 4 + 1;
  • 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 37 834 377(10), a positive integer number (with no sign),
converted from decimal system (from base 10)
and written as an unsigned binary (in base 2):

37 834 377(10) = 10 0100 0001 0100 1110 1000 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 37 834 376 converted from decimal system (from base 10) and written as an unsigned binary (in base 2) = ?

» Unsigned (positive) integer number 37 834 378 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)