Number Bases
Overview
You have ten fingers, so you count in tens, and so does everybody who has ever written a price or a date. There is nothing mathematically special about ten. It is an accident of anatomy, and the moment you notice that, the question changes from why would anyone count in twos to what would you count in if you were built out of switches.
This lesson covers the three number bases the specification names: decimal, base 10; binary, base 2; and hexadecimal, base 16. You will learn what a base actually is, why computers use binary to represent all data and instructions, why the same bit pattern can be a number, a letter, a pixel or part of a sound depending only on how it is read, and why hexadecimal is so often used in computer science. That last one has a trap in it that the specimen mark scheme explicitly rejects, and it is worth knowing before you write the obvious answer.
Objectives
- Understand the following number bases:
- decimal (base 10)
- binary (base 2)
- hexadecimal (base 16).
- Understand that computers use binary to represent all data and instructions.
- Explain why computers use binary to represent data and instructions Explain why hexadecimal is often used in computer science.
Mind map
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Lesson Note
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Lesson Evaluation
Congratulations on completing the lesson on 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.
- How many different digits does the hexadecimal number system use? A. 2 B. 10 C. 15 D. 16 Answer: D
- What is the decimal value of the hexadecimal digit C? A. 11 B. 12 C. 13 D. 14 Answer: B
- Which is the main reason computers use binary? A. Binary numbers are shorter than decimal ones B. Electronic components have two states that can be told apart reliably C. Binary uses less memory than decimal D. People find binary easier to read Answer: B
- Which answer would NOT be accepted as a reason for using hexadecimal instead of binary? A. It is easier to read B. It is quicker to type in C. It uses less memory D. It is less likely to be entered inaccurately Answer: C
- The bit pattern 01000001 is stored in memory. Which statement is correct? A. It must be the integer 65 B. It must be the character A C. It could be text, an image, a sound, an integer or an instruction D. It cannot be part of an image Answer: C
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