Base calculator

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Base calculator

I assume you are referring to calculating the result of a mathematical operation in a different number base. Here are the general steps to convert a number from one base to another:

  1. Start with the given number in the original base.
  2. Divide the number by the base you want to convert to.
  3. Write down the remainder.
  4. Divide the quotient from step 2 by the new base.
  5. Write down the new remainder.
  6. Repeat steps 4 and 5 until the quotient is 0.
  7. Write down the remainders in reverse order, and that is the number in the new base.

For example, let’s convert the number 1011 from base 2 to base 10:

  1. Start with the number 1011.
  2. Divide 1011 by 10: 1011 ÷ 10 = 101 with a remainder of 1.
  3. Write down the remainder: 1.
  4. Divide 101 by 10: 101 ÷ 10 = 10 with a remainder of 1.
  5. Write down the remainder: 1.
  6. Divide 10 by 10: 10 ÷ 10 = 1 with a remainder of 0.
  7. Write down the remainder: 0.
  8. Since the quotient is now 1, we repeat steps 4-7 with 1.
  9. Divide 1 by 10: 1 ÷ 10 = 0 with a remainder of 1.
  10. Write down the remainder: 1.
  11. Since the quotient is 0, we stop.
  12. Write down the remainders in reverse order: 1101.
  13. Therefore, the number 1011 in base 2 is equal to 13 in base 10.