4.5.4.4 Numbers with a fractional part Quiz: AQA Computer Science, Unit 5

The 20 questions

1. What is fixed point representation of a binary number?

   • A form that stores the exponent separately from the mantissa only
   • A form where the binary point stays in a fixed position among the bits
   • A form that stores each number as a sequence of decimal digits
   • A form that stores integers only in two's complement

2. What two parts are stored in the simplified floating point representation used at A level?

   • A sign and a base only
   • A numerator and a denominator
   • An integer part and a radix part only
   • A mantissa and an exponent

3. What decimal value does the first binary place after the point represent?

   • One eighth
   • One quarter
   • One tenth
   • One half

4. What is the decimal value of the binary fraction 0.11?

   • 0.875
   • 0.5
   • 0.75
   • 0.25

5. In this specification, how are the mantissa and exponent of a floating point number represented?

   • Using sign and magnitude
   • Using binary coded decimal
   • Using excess-128 only
   • Using two's complement

6. The specification says the IEEE standard need not be known. What representation is used instead?

   • The IEEE 754 single precision format, which stores a sign, an exponent and a fraction field
   • A fixed 32-bit integer with an implied decimal point, scaled by a constant power of ten
   • Binary coded decimal with an embedded decimal point, storing each decimal digit in four bits
   • A simplified floating representation consisting of a mantissa and an exponent

7. Convert decimal 5.75 to fixed point binary with 2 fractional bits.

   • 101.10
   • 101.01
   • 101.11
   • 110.11

8. Convert the binary number 110.101 to decimal.

   • 6.625
   • 5.625
   • 6.25
   • 6.5

9. Convert decimal 0.375 to binary.

   • 0.011
   • 0.110
   • 0.101
   • 0.111

10. Convert decimal 2.5 to 4-bit fixed point with 2 integer bits and 2 fractional bits.

    • 11.00
    • 01.10
    • 10.10
    • 10.01

11. A floating point value has mantissa 0.1011 and exponent 011 in base 2. What is its decimal value?

    • 11
    • 0.6875
    • 2.75
    • 5.5

12. A floating point value has mantissa 0.1100 and exponent 2 in base 2. What is its decimal value?

    • 0.75
    • 6
    • 1.5
    • 3

13. Convert decimal 0.625 to binary.

    • 0.100
    • 0.011
    • 0.110
    • 0.101

14. Convert decimal 13.5 to fixed point binary with 4 integer bits and 2 fractional bits.

    • 1101.01
    • 1101.10
    • 1011.01
    • 1110.10

15. A fixed point format uses 4 integer bits and 4 fractional bits. What are the largest value and the resolution?

    • Largest 15.0, resolution 1
    • Largest 15.9375, resolution 0.0625
    • Largest 16, resolution 0.5
    • Largest 15.9375, resolution 0.125

16. Which statement compares fixed point and floating point forms correctly?

    • Floating point stores every value exactly, while fixed point stores only approximations of the values
    • Fixed point gives a larger range, but floating point is always more precise than fixed point at any size
    • Floating point gives a much larger range for the same number of bits, but its precision depends on the mantissa length
    • Both give identical range and precision for equal numbers of bits, so the choice between them does not matter

17. A floating point value has mantissa 0.0011 and exponent 1 in base 2. What is its decimal value?

    • 0.375
    • 0.1875
    • 0.0625
    • 0.75

18. Why can a fractional value such as 0.2 not be stored exactly in binary fixed point with finitely many bits?

    • Binary cannot store any digit that comes after the point in a fixed number of bits at all
    • 0.2 is an irrational number, so it has no finite binary form and cannot be written as a fraction
    • Computers always round every fraction to the nearest integer, so decimals below one are lost entirely
    • Its binary form is a repeating fraction, 0.001100110011..., and so it never terminates

19. A fixed point format uses 3 integer bits and 2 fractional bits. What are the largest value and the resolution?

    • Largest 7.5, resolution 0.5
    • Largest 7.875, resolution 0.125
    • Largest 7.75, resolution 0.25
    • Largest 8, resolution 0.25

20. A fixed point format has 4 fractional bits. Which decimal value is stored exactly?

    • 0.8125, which is 13/16, a multiple of 1/16
    • 0.7, which is exact with four fractional bits in binary
    • 0.6, which is exact with four fractional bits in binary
    • 0.8, which is exact with four fractional bits in binary

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