A-LevelComputer ScienceData representation9618/33 · May/June 2025 · Q26 Marks
Numbers are stored in a computer using binary floating-point representation with: • 8 bits for the mantissa • 8 bits for the exponent • two's complement form for both the mantissa and the exponent.
- (a)Give the largest normalised positive two's complement binary number that can be stored in this system and state its denary equivalent. The denary answer should be expressed in terms of powers of 2. Mantissa Exponent Denary[2]
- (b)Calculate the normalised binary floating-point representation of –3.59375 in this system. Show your working. Working Mantissa Exponent[4]
Mark scheme
Marking points from the official mark scheme (May/June 2025). The mark or mark type is shown in brackets.
- [2] One mark for two's complement version and one mark for denary version
- Mantissa: 01111111
- Exponent: 01111111
- 127 x 2^120 // 0.9921875 x 2^127 // 127/128 x 2^127
- [4] One mark per mark point for working (Max 2)
- number converted to binary e.g., positive binary version of 3.59375 = (0)11.10011
- negative two's complement version - bits flipped and 1 added = 100.01101
- -4 + 1/4 + 1/8 + 1/32 // -4 + 025 +0.125 + 0.03125 // -(64 + 32 + 16 + 2 + 1)/32
- 2^2 (- 2^0 + 2^-4 + 2^-5 + 2^-7)
- One mark per mark point
- correct mantissa
- correct exponent, with working seen.
- Mantissa: 10001101
- Exponent: 00000010
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