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Number Theory

Number Theory Warmups

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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