Information representation：練習問題

If the colour depth of a bitmap image is increased from 1 bit (monochrome) to 8 bits, what is the effect on the number of available colours?

A computer uses a 10-bit register to store a fixed-point number in two's complement. The format uses 1 bit for the sign, 5 bits for the integer part, and 4 bits for the fractional part:
[ S | I | I | I | I | I . F | F | F | F ]
What is the denary equivalent of the binary pattern: 111111.1100?

A high-fidelity sound recording uses a sampling rate of \(96\text{ kHz}\) and a sampling resolution of \(24\text{ bits}\). The recording is stereo and lasts for \(10\text{ seconds}\).
Which expression gives the estimated file size in mebibytes (MiB)?

Which of the following binary bit patterns represents the denary integer \(-77\) stored in an 8-bit register using two's complement format?

Perform the following 8-bit two's complement addition:
\(01101100 + 00111001\)
What is the denary equivalent of the 8-bit result and does overflow occur?

A computer uses a character set to represent symbols. Explain how Unicode is able to represent more characters than the standard ASCII character set.

A graphic designer creates a company logo that needs to be scaled from a small business card to a large billboard without loss of quality.
Identify whether a vector graphic or a bitmapped graphic is more suitable for this purpose, and justify your choice.

A 24-bit True Colour bitmap image has a resolution of \(600 \times 400\) pixels. Calculate the file size in Mebibytes (MiB), assuming the file header is negligible.

A computer uses 8-bit registers to store data in various representations.
(a) Convert the hexadecimal value &D6 into an 8-bit unsigned binary number.
(b) Convert the hexadecimal value &D6 into a denary integer, assuming it represents an unsigned binary integer.
(c) Calculate the denary value of &D6, assuming it is stored as an 8-bit two's complement signed integer. Show your working.

Compression is used to reduce the size of files for storage or transmission.
(a) A text file contains the following sequence of characters:
AAAAABBBCCCCCDD
Show how Run-length Encoding (RLE) would compress this sequence.
(b) A user is streaming a high-definition movie over the internet. Justify the use of lossy compression rather than lossless compression in this specific situation.