Computer Science - 0478 CIE

Number Systems

Muhtasari

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.

Malengo

  1. 1 Understand how and why computers use binary to represent all forms of data
  2. 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. 3 Understand how and why hexadecimal is used as a beneficial method of data representation
  4. 4 (a) Add two positive 8-bit binary integers (b) Understand the concept of overflow and why it occurs in binary addition
  5. 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. 6 Use the two’s complement number system to represent positive and negative 8-bit binary integers

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Maelezo ya Somo

A computer cannot store the digit 7 or the letter A directly. It can only store the state of a switch, which is either on or off. We write on as 1 and off as 0, and a single one of these is called a bit. Group eight bits together and you have a byte. Because there are only two symbols, the system is called binary (base 2). Understanding binary is the foundation for almost everything else in the course, from how images are coded to how the processor adds.

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Tathmini ya Somo

Hongera kwa kukamilisha somo la Number Systems. Sasa kwa kuwa umechunguza dhana na mawazo muhimu, ni wakati wa kuweka ujuzi wako kwa mtihani. Sehemu hii inatoa mazoezi mbalimbali maswali yaliyoundwa ili kuimarisha uelewaji wako na kukusaidia kupima ufahamu wako wa nyenzo.

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  1. What is the denary value of the binary number 00011010? A. 24 B. 26 C. 28 D. 52 Answer: B
  2. Which hexadecimal value equals the binary number 11001001? A. C9 B. 9C C. CB D. B9 Answer: A
  3. 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
  4. 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
  5. 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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Vitabu Vinavyopendekezwa

Cambridge IGCSE and O Level Computer Science Coursebook
Cambridge IGCSE and O Level Computer Science Coursebook
Manukuu: Second edition
Mchapishaji: Cambridge University Press
Mwaka: 2021
ISBN: 978-1-108-91514-4
Maelezo: Endorsed coursebook with full coverage of the 0478/0984 syllabus, worked tasks and exam-style questions.
Cambridge IGCSE and O Level Computer Science
Cambridge IGCSE and O Level Computer Science
Manukuu: Second edition
Mchapishaji: Hodder Education
Mwaka: 2021
ISBN: 978-1-3983-1828-1
Maelezo: Endorsed textbook covering the theory and the algorithms, programming and logic content.

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