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O-LevelComputer ScienceData Representation2210/12 · Oct/Nov 2016 · Q57 Marks

5 A computer uses an 8-bit register. The 8-bit register contains binary integers. (a) Write the denary (base 10) value represented by: 128 64 32 16 8 4 2 1 0 1 1 1 0 0 0 0 (b) All the bits in the register are shifted one place to the right as shown below. 0 1 1 1 0 0 0 0 0 0 1 1 1 0 0 0 Write the denary number that is represented after this shift. (c) State the effect the shift to the right had on the original denary number from part (a). (d) The original number in part (a) is shifted three places to the right. (i) Show the new binary number: (ii) Write the equivalent denary number.

  1. (a)Write the denary (base 10) value represented by: 128 64 32 16 8 4 2 1 0 1 1 1 0 0 0 0[1]
  2. (b)All the bits in the register are shifted one place to the right as shown below. 0 1 1 1 0 0 0 0 0 0 1 1 1 0 0 0 Write the denary number that is represented after this shift.[1]
  3. (c)State the effect the shift to the right had on the original denary number from part (a).[1]
  4. (d)(i)The original number in part (a) is shifted three places to the right. Show the new binary number:[1]
  5. (d)(ii)Write the equivalent denary number.[1]
  6. (e)Describe the problems that could be caused if the original binary number in part (a) is shifted five places to the right.[2]

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Mark scheme

Marking points from the official mark scheme (Oct/Nov 2016). The mark or mark type is shown in brackets.

  1. [1] (a) 112
  2. [1] (b) 56
  3. [1] (c) divided by 2 // value 112 was halved // multiplied by 0.5
  4. [1] (d)(i) 0 0 0 0 1 1 1 0
  5. [1] (d)(ii) 14
  6. [2] (e) Any two from:
  7. run out of places to the right of register / at the end of register
  8. right-most 1 would be lost
  9. number would become 3 instead of 3.5
  10. loss of precision

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About this question

Topic
Data Representation, O-Level Computer Science (syllabus 2210). Structured question, 7 marks.
Source
O-Level Computer Science, Oct/Nov 2016 Paper 1 Variant 2, question 5.

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