A-LevelComputer ScienceData representation9618/32 · May/June 2025 · Q26 Marks
Numbers are stored in a computer using binary floating-point representation with: • 12 bits for the mantissa • 4 bits for the exponent • two's complement form for both the mantissa and the exponent.
- (a)Calculate the normalised binary floating-point representation of +124.4375 in this system. Show your working. Mantissa [empty cells for 12 bits] Exponent [empty cells for 4 bits] Working[3]
- (b)Calculate the denary value of the following normalised binary floating-point number. Show your working. Mantissa 1 0 1 0 0 0 1 0 1 0 1 1 Exponent 0 1 1 0 Working Denary value[3]
Mark scheme
Marking points from the official mark scheme (May/June 2025). The mark or mark type is shown in brackets.
- number converted to binary (0)1111100.0111
- use of exponent = 7 // Moving binary point the correct number (7) of places
- Mantissa 011111000111 Exponent 0111
- correct use of exponent seen
- correct conversion method from binary to denary
- Working: 1010001.01011 // moving bp 6 places to right
- Evaluation of two's complement -64 +16 + 1 + 0.25 + 0.0625 + 0.03125 // -64 + 16 + 1 + 1/4 + 1/16 + 1/32 // Converting two's complement back and evaluating positive binary number 32 + 8 + 4 + 2 + 0.5 + 0.125 + 0.03125 // 32 + 8 + 4 + 2 + 1/2 + 1/8 + 1/32
- Fractions methods - award both working marks for either (-2048 + 512 + 32 + 8 + 2 + 1) / 2048 x 26 = -1493 / 32 OR - 1 + 1/4 + 1/64 + 1/ 256 + 1/1024 + 1/2048 x 26 = -1493/32
- Answer: -46.65625 // -4621/32
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