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# Number Theory Warmups

If numbers aren't beautiful, we don't know what is. Dive into this fun collection to play with numbers like never before, and start unlocking the connections that are the foundation of Number Theory.

# Different Base

Express the base 4 number $$123_{4}$$ as a decimal number.

Convert the decimal number 96 to base 5.

If $$n$$ is a positive natural number, how many $$1$$'s will appear in the binary (base 2) representation of

$2^n + 1\text{?}$

What is the next natural number after $33_4\text{?}$

Which of the following is the binary (base 2) representation of $$\frac{7}{8}$$?

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