AQA GCSE Computer Science: Data Representation

A photographer is choosing settings for storing a digital image. Increasing the resolution or the colour depth improves how the image looks but also changes the file size.

Explain how resolution and colour depth each affect both the quality and the file size of a bitmap image. Your answer should explain what each term means and the trade-off the photographer must consider. (6 marks)

Answer each part, showing your working. All values are 8-bit unsigned binary.

(a) Convert the denary value $150$150 to 8-bit binary. (1 mark)

(b) Convert the binary value 10110100 to hexadecimal. (1 mark)

(c) Convert the hexadecimal value 5E to denary. (2 marks)

Two 8-bit unsigned binary numbers are added together:

  01001010
+ 00110001

(a) Perform the binary addition and give the 8-bit result. Show any carries. (2 marks)

(b) The two numbers 11010101 and 01000110 are then added. State the problem that occurs when these are added in an 8-bit register, and name this type of error. (1 mark)

A sound is recorded digitally. The recording uses:

• a sample rate of $8000$8000 Hz (samples per second)
• a bit depth of $16$16 bits
• a duration of $5$5 seconds

Use the formula $\text{file size} = \text{sample rate} \times \text{bit depth} \times \text{duration}$file size=sample rate×bit depth×duration.

(a) Calculate the file size of this recording in bits. (2 marks)

(b) Convert your answer to (a) into bytes. (1 mark)

An 8-bit unsigned binary number 00010110 (which is $22$22 in denary) undergoes a logical binary shift.

(a) Give the result of a logical shift left of 2 places applied to 00010110, as an 8-bit binary number. (1 mark)

(b) State the effect of a logical shift left of 2 places on the denary value of an unsigned binary number. (1 mark)

A character is stored using a character set such as ASCII.

State how many bits are used to store a single character in 7-bit ASCII, and how many different characters this can represent. (1 mark)