Real numbers are stored in a computer system using 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.

Mark scheme

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

1. [1] (a) Calculation of mantissa (e.g., 111.01 to 0111010000 or 1000110000 for -7.25 in two's complement)
2. [1] (a) Calculation or use of exponent (e.g., 0.11101 × 2^3 or 1.00011 × 2^3 or appropriate shifting)
3. [1] (a) Correct Answer: Mantissa 1000110000, Exponent 000011
4. [1] (b) Working for exponent (e.g., identifies 7 from 000111)
5. [1] (b) Working for mantissa (e.g., converts 1011000111 to 1.011000111 or similar, handles two's complement for negative)
6. [1] (b) Correct Answer: -78.25
7. [1] (c) Working (e.g., explaining shift of 6 places to the left for mantissa, -6 to exponent)
8. [1] (c) Correct Mantissa: 0111000000
9. [1] (c) Correct Exponent: 100001
10. [1] (d)(i) Requires 11 bits / more than 10 bits to store (accurately) / reference to maximum (positive) number that can be stored = 511
11. [1] (d)(i) Denary 513 in binary is 1000000001 // Normalised: 0.1000000001
12. [1] (d)(i) Results in overflow
13. [1] (d)(ii) The number of bits for the mantissa must be increased
14. [1] (d)(ii) 11/12 bits mantissa and 5/4 bits exponent