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News from Mathnasium of Hinsdale

11111100101

Jan 19, 2021

2021 in binary is 11111100101

Computers talk to each other in binary, a base system that uses only ones and zeros. We usually work in base ten, where we have 10 digits (0, 1, 2, 3, 4, 5, 6, 7, 8, 9). But let's think about the word binary. Compare it with other bi- words. How many wheels does a bicycle have? How many languages does a bilingual person speak? So, how many digits does a binary system use? (What other bi- words can you think of?)

Purple Math has a wonderful and detailed explanation of base 2 and base 10, and how to convert between the two. For a brief explanation, check out MathIsFun.

Fun Fact

(Yes, mathematicians like to have fun!) When you add the digits of a binary number together, an even sum is called an 'evil' number and and odd sum is called an 'odious' number. Let's look at 26 as an example. In binary, 26 is written 11010. Adding up the digits gives 1+1+0+1+0 = 3, and 3 is odd, so 26 is odious.

Don't worry! Numbers can't really be evil. It's just a play on words: even - evil and odd - odious. Is 2021 an evil or odious number? Check your work here (link).

Something Different

Turn your name into binary code with the help of ScienceFriday

Further Reading

Numbers Aplenty - 2021