Number Systems
Overview
Every photo, song, message and game on a computer is, underneath, nothing but ones and zeros. A computer is built from millions of tiny switches, and a switch has only two states: on or off. Binary is the language those switches speak, and once you can read it you can see how any kind of data is really stored.
In this lesson you will convert fluently between denary, binary and hexadecimal, add binary numbers and spot when they overflow, shift bits to multiply and divide by two, and use two's complement to write negative numbers in binary. These are the most reliable marks in the whole paper because the method is fixed: learn it once and you can never be caught out.
Objectives
- 1 Understand how and why computers use binary to represent all forms of data
- 2 (a) Understand the denary, binary and hexadecimal number systems (b) Convert between (i) positive denary and positive binary (ii) positive denary and positive hexadecimal (iii) positive hexadecimal and positive binary
- 3 Understand how and why hexadecimal is used as a beneficial method of data representation
- 4 (a) Add two positive 8-bit binary integers (b) Understand the concept of overflow and why it occurs in binary addition
- 5 Perform a logical binary shift on a positive 8-bit binary integer and understand the effect this has on the positive binary integer
- 6 Use the two’s complement number system to represent positive and negative 8-bit binary integers
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Lesson Note
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Lesson Evaluation
Congratulations on completing the lesson on Number Systems. 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 denary value of the binary number 00011010? A. 24 B. 26 C. 28 D. 52 Answer: B
- Which hexadecimal value equals the binary number 11001001? A. C9 B. 9C C. CB D. B9 Answer: A
- A logical shift one place to the right has what effect on a positive binary number? A. multiplies it by 2 B. divides it by 2 C. adds 1 D. inverts the bits Answer: B
- Why do computers use binary to represent data? A. it stores more data than denary B. their switches have only two states C. it is the same as hexadecimal D. humans find it easy to read Answer: B
- An 8-bit register holds 11111111 and 1 is added. The result is: A. stored correctly as 256 B. an overflow error C. shifted left D. converted to hex Answer: B
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