A-LevelComputer ScienceData representation9618/32 · May/June 2023 · Q15 Marks
Numbers are stored in a computer using floating point representation with: • 10 bits for the mantissa • 6 bits for the exponent • two's complement form for both the mantissa and exponent.
- (a)Write the normalised floating-point representation of the following binary number using this system: 0101010.111 Show your working. Working Mantissa Exponent[2]
- (b)Describe the reason why the normalised form of the following binary number cannot be represented accurately using this system. 0101011.111001[3]
Mark scheme
Marking points from the official mark scheme (May/June 2023). The mark or mark type is shown in brackets.
- [2] One mark per mark point • correct mantissa • correct exponent with associated working Answer Mantissa 0 1 0 1 0 1 0 1 1 1 Exponent 0 0 0 1 1 0 Working exponent = 6 (movement of 6 bicimal places seen to find what exponent should be) calculation of denary 6 to binary (000)110
- [3] One mark per mark point (Max 3) MP1 the mantissa of the number would need to be 0.101011111001 / 13 bits / digits MP2 ... it can only store 10 bits / digits MP3 The 3 least significant digits would be truncated MP4 ...causing a loss of precision
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