A-LevelComputer ScienceData representation9618/32 · Oct/Nov 2022 · Q16 Marks
Normalised floating-point numbers are stored in a computer system using two's complement for both the mantissa and the exponent with: • 11 bits for the mantissa • 5 bits for the exponent.
- (a)Write the largest positive two's complement binary number that can be stored in this system. Mantissa [Figure X.X] Exponent [Figure X.X][1]
- (b)Calculate the denary value of the given binary floating-point number. Show your working. Mantissa [Figure X.X] Exponent [Figure X.X][3]
- (c)State when underflow occurs in a binary floating-point system.[2]
This question uses a diagram from the original paper, which isn't shown here. Open the full paper from the past papers archive to see it.
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2022). The mark or mark type is shown in brackets.
- [1] (a) Mantissa: 01111111111 Exponent: 01111
- [2] (b) Two marks for working • correct calculation of exponent seen • correct application of exponent to mantissa seen
- [1] (b) One mark for correct answer Working: = 1.0110010011 × 29 //exponent = 9 = 1011001001.1 (moving bp 9 places to right) // evaluate two's complement For example: -512 + 128 + 64 + 8 + 1 + 0.5 Answer: -310.5 //-310½
- [1] (c) One mark per point • Following an arithmetic/logical operation
- [1] (c) the result is too small to be precisely represented in the available system // When the number of bits is not enough / too small for the computer’s allocated word size / to represent the binary number
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