35 Base conversion
Let’s return to the concept of our decimal place system.
Much of our intuition is built around this, and as we have seen, our measurement systems take advantage of its structure.
However considering bases other than 10 can give us a deeper understanding into how our standard place-value system works.
What’s the time?
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Suppose someone makes a fun watch.
The watch shows the hours and minutes in binary. So, for example, 1:18 in the afternoon, might be written as 1101:10010. What would the binary watch show at 7:43 in the evening? How many digits would we need to be able to show all times of day? |
Base conversion exercises
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QuizHave a go at the following online quiz for converting between base 10 and binary or base 5 numbers.
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Stop and thinkRecall that when we are adding base 10 numbers, we can add the numbers in each column and then use remainders to do the entire sum. Could you devise a similar system in a different base? |
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CodingWhat are the steps for converting a given number in base 10 into base 5? Can you write out the steps clearly? Could you write Scratch code for this? (Hint: some key operators to use are the “floor” and “mod” blocks). See a worked example here. |
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SummariseWrite out your step-by-step process for converting from other bases (use your code from the Coding activity if you completed it). Read over your step-by-step process and consider whether it would make sense to someone who hasn’t studied this course, and refine the description so that it’s clear and without too much jargon or terminology. Check that the process works with an example, and make any adjustments if required. |
