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course Mth 151
7/19 1
Question: `q001. There are 5 questions in this set.
The preceding calculations have been done in our standard base-10 place value system. We can do similar calculations with bases other than 10.
For example, a base-4 calculation might involve the number 3 * 4^2 + 2 * 4^1 + 1 * 4^0. This number will be expressed as 321{base 4}.
What would this number be in base 10?
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Your solution:
3*10^2 + 2 * 10 ^ 1 + 1 * 10 ^ 0 this number would be expressed 321 { base 10 }
3
Why is the 4 still the base when it is written in base 10 form???
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Question: `q002. What would the number 213{base 4} be in base 10 notation?
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Your solution:
213{base 4} means 2 * 4^2 + 1 * 4^1 + 3 * 4^0
213 {base 10} 2 * 16 + 1 * 4 + 3 * 1 = 32 + 4 + 3 = 39
3
Ok
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Question: `q003. Suppose we had a number expressed in the form 6 * 4^2 + 7 * 4^1 + 3 * 4^0. This number isn't quite in the form needs to be if it is to be expressed in base 4. This is because we have the numbers 6 and 5, which exceed 4. How would this number be expressed without using any numbers 4 or greater?
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Your solution:
1 * 4^3 + 3 * 4^2 + 3 * 4^1 + 3 * 4^0
3
Ok
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Question: `q004. What would happen to the number 1333{base 4} if we added 1?
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Your solution:
It would be 11333 {base 4}
3
Explain how having another 4^1 would change the entire answer
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Question: `q005. How would the decimal number 659 be expressed in base 4?
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Your solution:
659 = 2 * 4^4 + 2 * 4^3 + 1 * 4^2 + 0 * 4^1 + 3 * 4^0.
3
Ok
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