A-LevelComputer ScienceData representation9618/31 · May/June 2025 · Q26 Marks
Numbers are stored in a computer using binary floating-point representation with: • 10 bits for the mantissa • 6 bits for the exponent • two's complement form for both the mantissa and the exponent.
- (a)Write the normalised floating-point representation of the following binary number using this system. 0.00000011010111 Mantissa [empty boxes] Exponent [empty boxes][2]
- (b)Calculate the normalised binary floating-point representation of –25.3125 in this system. Show your working. Working Mantissa [empty boxes] Exponent [empty boxes][4]
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Mark scheme
Marking points from the official mark scheme (May/June 2025). The mark or mark type is shown in brackets.
- [1] Correct mantissa: 0110101110
- [1] Correct exponent: 111010
- [1] number converted to binary e.g., positive binary version of 25.3125 = (0)11001.0101
- [1] two's complement version bits flipped and 1 added = 100110.1011
- [1] -32 +4 +2 +0.5 + 0.125 + 0.0625 // -32 + 4 + 2 + 1/2 + 1/8 + 1/16
- [1] movement of binary point seen (5 places)
- [1] correct mantissa: 1001101011
- [1] correct exponent: 000101
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