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Excel in math and science

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Excel in math and science

Master concepts by solving fun, challenging problems.

It's hard to learn from lectures and videos

Learn more effectively through short, interactive explorations.

Used and loved by over 6 million people

Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.

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Number Bases

Concept Quizzes

Number Bases Warmup
Alternate Bases
Binary Numbers
Hexadecimal Numbers
Arithmetic in Base N
Integer Number Bases

Challenge Quizzes

Level 1
Level 2
Level 3
Level 4
Level 5

Alternate Bases

Express the base 4 number \(123_{4}\) as a decimal number.

\[ 27 \] \[ 123 \] \[ 23\] \[ 108\]

Show explanation

by Brilliant Staff

Convert the decimal number 96 to base 5.

\[ 442_{5} \] \[ 441_{5} \] \[ 1031_{5} \] \[ 341_{5} \]

Show explanation

by Brilliant Staff

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

\[2^n + 1\text{?}\]

1 2 3 4

Show explanation

by Brilliant Staff

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

\[ 3330_{4} \] \[ 100_{4} \] \[ 1000_{4} \] \[ 332_{4} \]

Show explanation

by Brilliant Staff

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

\[ 0.001_{2} \] \[ 0.101_{2} \] \[ 1.001_{2} \] \[ 0.111_{2} \]

Show explanation

by Brilliant Staff

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