Data Representation：練習問題

When representing character data, which statement best describes a reason for choosing Unicode (UTF-16) over standard ASCII?

A floating-point representation uses a \(10\)-bit two's complement mantissa and a \(6\)-bit two's complement exponent. A number is stored with the following bit pattern:
Mantissa: \(0.101100000_2\)
Exponent: \(000101_2\)
What is the denary equivalent of this floating-point value?

A random-access file uses a hashing algorithm to determine the address of records. When a collision occurs, the system uses progressive overflow (linear probing). How does this method resolve the collision?

What is the correct value for one Kibibyte (KiB)?

Consider the addition of two 8-bit two's complement signed integers:
\( X = 01101011_{2} \)
\( Y = 00100101_{2} \)
Perform the addition and identify the result and whether an overflow has occurred.

Convert the denary number \( 156 \) into its hexadecimal equivalent, showing the intermediate steps used in the conversion process.

Explain the difference in the number of bytes between \( 1 \text{ Gibibyte (GiB)} \) and \( 1 \text{ Gigabyte (GB)} \), and identify which unit represents the larger amount of data.

Explain the specific conditions under which an arithmetic overflow occurs when adding two signed 8-bit integers in two's complement form.

Hexadecimal is frequently used in low-level computing for tasks such as specifying memory addresses or hardware identifiers.
(a) State two advantages of using hexadecimal over binary when representing data for a human programmer.
(b) A hardware device has the identifier C4-5D. Convert the hexadecimal value C4 into a denary integer and 5D into an 8-bit unsigned binary integer.

A company needs to store a large collection of high-resolution architectural drawings. The technical team must choose between bitmap and vector graphic formats.
(a) Explain why a vector graphic format would be more suitable than a bitmap format for a logo that needs to be scaled to fit on both a business card and a large billboard.
(b) Describe two items of data that would be stored in the file header of a bitmap image.
(c) A bitmap image has a resolution of \( 1024 \times 768 \) pixels and a colour depth of \( 8 \text{ bits} \). Calculate the minimum file size in MiB. Show your working.