A-LevelComputer ScienceData representation9618/31 · Oct/Nov 2022 · Q19 Marks

Real numbers are stored in a computer system using floating-point representation with: • 8 bits for the mantissa • 8 bits for the exponent • two's complement form for both mantissa and exponent.

(a)Write the normalised floating-point representation of +202 in this system. Show your working.[3]
(b)Write the normalised floating-point representation of -202 in this system. Show your working.[3]
(c)(i)A binary number is stored in the computer system. Mantissa 0 0 0 1 1 1 1 0 Exponent 0 0 0 1 1 0 0 0 State why the number is not normalised.[1]
(c)(ii)Write the normalised floating-point representation of the number.[2]

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Mark scheme

Marking points from the official mark scheme (Oct/Nov 2022). The mark or mark type is shown in brackets.

[2] Two marks for working
One mark for correct answer
Working: Conversion to binary + 202 = 11001010 // repeated division by 2 // 128 + 64 + 8 + 2
Appropriate shifting of binary point for + 202 = 0.1100101 × 28 // exponent = 8
Answer: = 01100101 00001000 (stored as mantissa and exponent)
[2] Two marks for working
One mark for correct answer
Working: • Appropriate method of conversion e.g.
= 10011010 (one's complement of 8-bit mantissa)
= 10011011 (two's complement of 8-bit mantissa)
-256 + 32 + 16 + 4 +2
• Realisation that the exponent doesn't change // value of exponent = 8 // appropriate shifting of binary point
Answer: = 10011011 00001000 (stored as mantissa and exponent)
The mantissa does not begin with 01/10 (as its most significant bits)
// the mantissa begins with 00 // first two digits are the same.
[1] One mark for each point: Correct mantissa, Correct exponent
Mantissa: 0 1 1 1 1 0 0 0
Exponent: 0 0 0 1 0 1 1 0

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