A-LevelComputer ScienceData representation9618/31 · Oct/Nov 2023 · Q15 Marks
Real numbers are stored in a computer using floating-point representation with: • 12 bits for the mantissa • 4 bits for the exponent • two's complement form for both the mantissa and exponent.
- (a)Write the normalised floating-point representation of +65.25 in this system. Show your working. Mantissa Exponent[3]
- (b)Explain the problem that will occur in storing the normalised floating-point representation of +65.20 in this system.[2]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2023). The mark or mark type is shown in brackets.
- [1] One mark for working (Max 1) conversion of 65.25 to binary seen e.g. 1000001.01 = 65.25 // 64+1 +0.25 / ¼
- [1] One mark per mark point (Max 2) correct mantissa
- [1] correct exponent
- [1] MP1 the decimal fraction 0.20 cannot be represented exactly (the closest is 0.25 / 0.1875)
- [1] MP2 therefore, there will be a loss of precision due to a rounding error/truncation
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