Numbers are stored in a computer using floating-point representation with: • 12 bits for the mantissa • 4 bits for the exponent • two's complement form for both the mantissa and exponent.

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2021). The mark or mark type is shown in brackets.

1. [2] One mark for each correct marking point (Max 2)
2. • 010111000110 (correct mantissa)
3. • 0111 (correct exponent)
4. [2] One mark for each correct consequence
5. One mark for each correct justification
6. Consequence
7. • The precision/accuracy of the number would be reduced
8. Justification
9. • because the least significant bits of the original number have been truncated/lost // the original number had 13 bits / 14 bits with sign but the mantissa can only store 12 bits
10. [3] One mark for each correct marking point (Max 3)
11. • To store the maximum range of numbers in the minimum number of bytes / bits
12. • Normalisation minimises the number of leading zeros/ones represented
13. • Maximising the number of significant bits // maximising the (potential) precision / accuracy of the number for the given number of bits
14. • ... enables very large / small numbers to be stored with accuracy.
15. • Avoids the possibility of many numbers having multiple representations.