Exploring Number Bases
A worksheet for 6th graders to explore different number bases, including base 10 and base 2.
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Exploring Number Bases
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Read each question carefully and answer to the best of your ability. Show your work where necessary.
Our everyday number system is called Base 10 (or the decimal system). It uses ten digits (0-9). Other number systems use a different number of digits. For example, Base 2 (or the binary system) uses only two digits (0 and 1).
1. The number system we use every day is called Base .
2. Base 2 uses only the digits and .
3. In Base 10, the place values are powers of .
4. What are the first three place values (from right to left) in Base 10?
5. Which of the following numbers is written in Base 2?
102
210
101
112
To convert from Base 2 to Base 10, multiply each digit by its place value (powers of 2) and add the results.
6. Convert the Base 2 number 1011₂ to Base 10. Show your work.
7. The number 7 in Base 10 is represented as 111₂ in Base 2.
True
False
8. Write the Base 10 number 13 as a Base 2 number. Show your work.