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Answers
Topic
- Base conversion
Understanding the Problem
① The 1 in each digit has a place value of the power of the base. The exponent of the numbers is in descending order.
② The conversion of the base can be done by repeated division.
③ Let the quotient be the greatest digit and list the remainders in ascending order.
Solution
(1)
Divide by 4,
⇒ Quotient 43, remainder 3.
Dividing the quotient by 4.
⇒ Quotient 10, remainder 3.
Again,
⇒ Quotient 2, remainder 2.
(2)
In base 10,
(3)
Divide by 2,
⇒ Quotient 37, remainder 1.
Dividing the quotient by 2.
⇒ Quotient 18, remainder 1.
Again,
⇒ Quotient 9, remainder 0.
Keep repeating,
⇒ Quotient 4, remainder 1.
⇒ Quotient 2, remainder 0.
⇒ Quotient 1, remainder 0.
Let the quotient be the greatest digit, and list the remainders in ascending order.
(4)
Using the same process,
⇒ Quotient 25, remainder 0.
Dividing the quotient by 3.
⇒ Quotient 8, remainder 1.
Again,
⇒ Quotient 2, remainder 2.
(5)
Let's bring this number into base 10.
Using the repeated division by 4,
⇒ Quotient 10, remainder 2
⇒ Quotient 2, remainder 2
More Information
- Why do we use repeated division?
The reason comes from the process of repeated division. Say, we are dividing 42 by 5 repeatedly.
⇒ Quotient 8, remainder 2
⇒ Quotient 1, remainder 3
Further simplifying,
If we see it through, we can see all the place values are in terms of base 5. So, this is why we use the repeated division process for base conversion.