Converting Between Number Bases
Overview
The specimen paper opens with two questions worth one mark each. Convert 107 to binary. Convert 10011100 to hexadecimal. There is no working to award marks for and no partial credit to hope for: the answer is right or it is not, and no calculator is allowed on either paper. Conversions are the cheapest marks on this qualification and the easiest to throw away.
This lesson covers all six conversions the specification requires, in both directions between binary and decimal, between binary and hexadecimal, and between decimal and hexadecimal. You will learn a reliable method for each, a check for each, and the reason one pair of them is trivially easy while the other two need real work. Everything here stays inside the range the specification fixes: decimal 255, binary 1111 1111 and hexadecimal FF, which are the same whole number written three ways.
Objectives
- Understand how binary can be used to represent whole numbers. Understand how hexadecimal can be used to represent whole numbers. Be able to convert in both directions between:
- binary and decimal
- binary and hexadecimal
- decimal and hexadecimal.
Mind map
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Lesson Note
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Lesson Evaluation
Congratulations on completing the lesson on Converting Between Number Bases. Now that youve explored the key concepts and ideas, its time to put your knowledge to the test. This section offers a variety of practice questions designed to reinforce your understanding and help you gauge your grasp of the material.
You will encounter a mix of question types, including multiple-choice questions, short answer questions, and essay questions. Each question is thoughtfully crafted to assess different aspects of your knowledge and critical thinking skills.
Use this evaluation section as an opportunity to reinforce your understanding of the topic and to identify any areas where you may need additional study. Don't be discouraged by any challenges you encounter; instead, view them as opportunities for growth and improvement.
- What is the decimal number 37 in binary? A. 00100101 B. 00101001 C. 00110101 D. 01001010 Answer: A
- What is the binary number 11001010 in hexadecimal? A. AC B. C9 C. CA D. DA Answer: C
- What is the hexadecimal number 2B in decimal? A. 22 B. 41 C. 43 D. 47 Answer: C
- How many bits does one hexadecimal digit correspond to? A. 2 B. 4 C. 8 D. 16 Answer: B
- What is the largest decimal value that can be represented using 8 bits? A. 128 B. 255 C. 256 D. 512 Answer: B
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