Fundamentals of Data Representation

Question 1

How does the bit pattern indicate that a number is normalised?

Answer 1

The 2 starting bits are either, 10 or 01.

Question 2

What are the advantages of using normalised floating point form?

Answer 2

• Maximises precision/accuracy for a given number of bits.

- Offers a unique representation of each number.

Question 3

What is the smallest negative and largest positive value possible on a twos complement floating point number?

Answer 3

Negative: Positive:

111111. ..… Mantissa 01111…… Mantissa
111112. ..… Exponent 01111…… Exponent

Question 4

What is the largest negative and smallest positive value possible on a twos complement floating point number?

Answer 4

Negative: Positive:

11111. ..… Mantissa 000……1 Mantissa
11112. ..… Exponent 100…… Exponent

Question 5

Explain why the relative error is usually considered to be a more important measure of error than the absolute error.

Answer 5

The impact of an error depends on its size relative to the number that is represented
(the error is more significant the smaller the represented number becomes)

Question 6

Why do vector graphics use less storage than bitmapped graphics?

Answer 6

• Vector graphics use less storage as they don’t need to store the colour of each pixel
• Vector graphics store information about / properties of the objects that an image is composed of - It takes only a small amount of memory to store the properties of an object
• A single object might be equivalent to many pixels

Question 7

What are the advantages of vector graphics vs bitmapped graphics?

Answer 7

• Individual parts of the image can be edited independently
• Fewer bytes are used to represent an image
• If an object is deleted, the software knows what is behind it (no “hole” is left in the image)