A LevelComputer ScienceCambridge (CIE)Exam Questions13. Data RepresentationFloating-point Numbers, Representation & Manipulation

Floating-point Numbers, Representation & Manipulation (Cambridge (CIE) A Level Computer Science): Exam Questions

Exam code: 9618

34 mins6 questions
1a
3 marks

Numbers are stored in a computer using binary 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.

Calculate the normalised binary floating-point representation of +201.125 in this system.

Show your working.

Mantissa

Exponent

How did you do?

1b
3 marks

Calculate the denary value of the given normalised binary floating-point number.

Show your working.

Mantissa

1

0

1

0

1

1

0

0

1

1

Exponent

0

0

0

1

0

1

How did you do?

2a
2 marks

Numbers are stored in a computer using binary floating‑point representation with:

  • 12 bits for the mantissa

  • 4 bits for the exponent

  • two’s complement form for both the mantissa and the exponent.

Calculate the denary value of the given normalised binary floating‑point number.

Show you working.

Mantissa

0

1

0

0

0

1

1

1

0

1

1

1

Exponent

0

1

1

1

How did you do?

2b
4 marks

Calculate the normalised binary floating‑point representation of – 49.1875 in this system.

Show your working.

Mantissa

Exponent

How did you do?

3a
3 marks

Real numbers are stored in a computer system 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.

Calculate the denary value of the given normalised floating-point number.

Show your working.

Mantissa

0

1

0

0

1

1

1

1

0

0

Exponent

0

0

1

0

0

1

How did you do?

3b
3 marks

Calculate the normalised floating-point representation of –102.75 in this system. Show your working.

Mantissa

Exponent

How did you do?

4a
2 marks

Describe the effect of changing the allocation of bits used for the mantissa and for the exponent in a floating-point number with a fixed total number of bits.

How did you do?

4b
3 marks

Real numbers are stored in a computer, using floating-point representation with:

  • 12 bits for the mantissa

  • 4 bits for the exponent

  • two’s complement form for both the mantissa and exponent.

Calculate the normalised floating-point representation of +54.8125 in this system.

Show your working.

Mantissa

Exponent

How did you do?

5a
3 marks

Real numbers are stored in a computer system using floating-point representation with:

  • 12 bits for the mantissa

  • 4 bits for the exponent

  • two’s complement form for both the mantissa and the exponent.

Write the normalised floating-point representation of +65.25 in this system.

Show your working.

Mantissa

Exponent

How did you do?

5b
2 marks

Explain the problem that will occur in storing the normalised floating-point representation of +65.20 in this system.

How did you do?

6a
3 marks

Real numbers are stored in a computer system 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.

Write the normalised floating-point representation of -96.75 in this system.

Show your working.

Mantissa

Exponent

How did you do?

6b
3 marks

Explain why a binary representation is sometimes only an approximation to the real number it represents.

How did you do?