4.5.4.7 Range, precision and normalisation of floating point Quiz: AQA Computer Science, Unit 5

The 20 questions

1. For a given total number of bits, which form provides the larger range?

   • Fixed point
   • Floating point
   • Pure binary
   • Character code

2. What property of a floating point representation is determined by the number of mantissa bits?

   • Range
   • Precision
   • Overflow limit
   • Calculation speed

3. What is the primary purpose of normalising a floating point number?

   • Increase speed
   • Maximise range
   • Maximise precision
   • Prevent underflow

4. What are the first two bits of a normalised positive floating point mantissa?

   • 0.0
   • 1.0
   • 0.1
   • 1.1

5. What is the main processing advantage of fixed point over floating point representation?

   • Variable point
   • Greater precision
   • Larger range
   • Faster calculations

6. What is the main disadvantage of fixed point representation compared to floating point?

   • Unstable precision
   • Limited range
   • Slower speed
   • Complex hardware

7. Which component of a floating point number determines its range?

   • Mantissa
   • Exponent
   • Sign bit
   • Parity bit

8. Normalise the mantissa 0.0110 with exponent 3 in base 2. What is the normalised form?

   • 0.0011 with exponent 4
   • 0.0110 with exponent 3
   • 0.1100 with exponent 4
   • 0.1100 with exponent 2

9. Normalise the mantissa 0.0001 with exponent 5 in base 2. What is the normalised form?

   • 0.1000 with exponent 2
   • 0.0001 with exponent 5
   • 0.0010 with exponent 3
   • 0.1000 with exponent 8

10. What aspect of a floating point representation is directly limited by mantissa size?

    • Precision
    • Range
    • Speed
    • Exponent bias

11. Using 8 bits in fixed point with 6 integer bits and 2 fractional bits, what is the largest unsigned value?

    • 255
    • 63.75
    • 16
    • 63

12. A normalised mantissa is 0.1011 with exponent 4 in base 2. What is its decimal value?

    • 11
    • 2.75
    • 0.6875
    • 5.5

13. What bit must immediately follow the binary point in a normalised positive mantissa?

    • 1
    • Sign bit
    • Exponent bit
    • 0

14. What is the decimal value of the fixed point number 0010.1100 with 4 integer bits and 4 fractional bits?

    • 2.75
    • 3.25
    • 2.5
    • 10.75

15. A fixed point format has 4 integer bits and 2 fractional bits. What is the smallest positive step between values?

    • 0.5
    • 1
    • 0.25
    • 0.125

16. How does normalisation prevent precision loss in floating point numbers?

    • Adds exponent bits
    • Extends sign bit
    • Removes leading zeros
    • Rounds least significant

17. What is the effect of reallocating mantissa bits to the exponent in floating point?

    • Greater range, greater precision
    • Less range, greater precision
    • Greater range, less precision
    • Less range, less precision

18. A normalised mantissa is 0.1101 with exponent -2 in base 2. What is its decimal value?

    • 0.8125
    • 0.40625
    • 3.25
    • 0.203125

19. Why is fixed point representation often chosen for simple embedded systems?

    • Simpler calculation hardware
    • Automatic normalisation
    • Higher floating precision
    • Maximum dynamic range

20. What is the maximum decimal value that can be stored in an unsigned 16-bit integer?

    • 65535
    • 32767
    • 1000000
    • 65536

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