Binary, Decimal, Hexadecimal Conversions: Practice Problems

📚 Topic Summary

Number systems are essential in computer science. We commonly use the decimal system (base-10), but computers operate using the binary system (base-2). Hexadecimal (base-16) is often used as a shorthand for representing binary data. Converting between these systems is a fundamental skill for programmers and anyone working with computer hardware or software. Practicing these conversions helps you understand how data is represented at a low level. This knowledge allows you to work more effectively with system configurations and debug errors.

🧠 Part A: Vocabulary

Match the term with its definition:

1. Term: Binary
2. Term: Decimal
3. Term: Hexadecimal
4. Term: Base
5. Term: Bit

1. Definition: A single binary digit (0 or 1).
2. Definition: The number of unique digits used to represent numbers in a number system.
3. Definition: A number system with base 16, using digits 0-9 and A-F.
4. Definition: A number system with base 2, using digits 0 and 1.
5. Definition: A number system with base 10, using digits 0-9.

(Match each term above to its corresponding definition.)

📝 Part B: Fill in the Blanks

Complete the following sentences:

The binary system uses only two digits: _____ and _____. Converting from decimal to binary involves repeated _____. In hexadecimal, the letter A represents the decimal number _____. The hexadecimal number 10 is equal to the decimal number _____. Computers primarily use the _____ system for internal operations.

🤔 Part C: Critical Thinking

Explain why hexadecimal is often used to represent binary data, instead of directly using binary. What are the advantages of using hexadecimal representation?