Real numbers are stored in a computer 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 (Oct/Nov 2023). The mark or mark type is shown in brackets.

1. [1] conversion of -96.75 to binary e.g., positive 96.75, flip the bits + 1 to give 10011111.01 // -128+16+8+4+2 + 1 + 0.25 / ½ seen
2. [1] correct mantissa (1001111101)
3. [1] correct exponent (000111)
4. [1] Real numbers (can) have a fractional part (such as 1/3 and 1/2) / (such as 0.4 and 0.25)
5. [1] The fixed length of the storage means that you can't store very large / very small numbers
6. [1] Binary numbers represent numbers based on powers of 2, with limited fractional representations such as 1/2, 1/4, 1/8, 1/16, etc.
7. [1] It isn't possible to store all fractions with the level of precision provided by this system
8. [1] ...the fractional part of the number is as close as possible within these constraints.