Numbers are stored in two different computer systems by using floating-point representation. System 1 uses: • 10 bits for the mantissa • 6 bits for the exponent • two's complement form for both the mantissa and the exponent. System 2 uses: • 8 bits for the mantissa • 8 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 2023). The mark or mark type is shown in brackets.

1. [4] (a) One mark per mark point (Max 4) • conversion of 113.75 to binary seen 1110001.11 • exponent for normalisation 7 converted to binary 111 // evidence of binary point moved 7 places // evidence of finding exponent = 7 • system 1 answer Mantissa: 0111000111 Exponent: 000111 • system 2 answer showing correct version from system 1 Mantissa: 01110001 Exponent: 00000111
2. [2] (b) One mark per mark point (Max 2) • the mantissa in system 2 does not have enough bits to store the whole binary number // 10 bits required and only 8 bits available • so precision is lost / the number is truncated