Units of Information (AQA GCSE Computer Science)

Explain how a binary number can be multiplied by 8 by shifting bits.

Using the Huffman code in Figure 3, complete the table to show the Huffman coding for the characters O, SPACE and B.

Figure 3

Using Huffman coding, the text ZOE SAW A ZEBRA AT THE ZOO can be stored in 83 bits.

Calculate how many additional bits are needed to store the same piece of text using ASCII.

Show your working.

A sound engineer is recording a singer.

Describe why the sound must be converted to a digital format before it can be stored on a computer system.

The sound engineer is using a sampling rate of 2000 Hz and a sample resolution of 4 bits.

What is the minimum file size of a 5-second recording? Your answer should be given in bytes.

You should show your working.

Convert 16,000,000 bits to megabytes (MB).

You should show your working.

A sampling rate of 20,000 Hz and a sample resolution of four bits is used to make a digital recording of a sound that lasts 50 seconds.

What is the minimum file size of the recording in megabytes (MB)?

You should show your working.

Figure 1 shows a 5 pixel x 5 pixel image. A minimum colour depth of two bits is needed to store the image.

Figure 1

Explain how the image in Figure 1 can be represented as a bitmap.

A 10 pixel x 10 pixel image contains five different colours.

Calculate the minimum file size, in bits, of this image when represented as a bitmap.

You should show your working.

A black and white image has been compressed using run length encoding (RLE).

The first bit in each byte of the bit pattern represents the colour and the remaining seven bits of the byte represent the number of pixels in the run.

The image has a run of 60 black pixels followed by a run of 30 white pixels and is represented by the bit pattern shown in Figure 2.

Figure 2

Using the same RLE method, give the bit pattern for a black and white image that has a run of 64 white pixels followed by a run of 15 black pixels.

Add together the following three binary numbers and give your answer in binary.

How many bits are there in two kilobytes?

Show your working.

Figure 1 shows a 10 x 8 bitmap image that uses three colours.

Calculate the minimum file size that would be required to store the bitmap image in Figure 1.

Give your answer in bytes.

Show your working.

Analogue sound must be converted to a digital form for storage and processing in a computer.

A 50-second sound has been recorded at a sample rate of 40000 Hz.

Two bytes have been used to store each sample of the sound.

Calculate the file size of the sound file in megabytes.

Show your working.

Another method for compressing data is Huffman coding. In Huffman coding, the codes for the characters can be created based on their position in a tree.

Figure 3 shows a Huffman code for each different character in the string in Figure 2.

Figure 3

Complete the Huffman tree below to show the position of the characters I, S and P using the codes from Figure 3.

Calculate the minimum file size in bits of a 10 pixel by 10 pixel image with a colour depth of 3 bits.

Calculate the minimum file size in bytes of a 10 pixel by 10 pixel image with 12 different colours.

You should show your working.

Figure 1 shows a value represented as a bit pattern.

Figure 1

1 0 1 1 0 0 0 0

A binary shift can be used to divide the value in Figure 1 by 4

State the result of this shift?

Your answer must be in binary.

Add the following binary numbers and give your answer in binary

Eight minutes of sound has been digitally recorded. The sampling rate used was 25 000 Hertz and the sample resolution used was 4 bits.

Calculate the minimum file size for the recording.

Give your answer in megabytes.

You should show your working.

Explain what effects increasing the sampling rate would have on the recording.

Run Length Encoding (RLE) is represented using binary, with one bit representing the colour (W = 1, B = 0) followed by seven bits representing the frequency.

Give the binary representation of the RLE: B15 W9

Table 1 is a frequency table that contains the frequency of characters in a string.

Table 1

Use the frequencies given in Table 1 to draw a Huffman tree that represents the string.

Figure 2 shows a string.

Figure 2

MISSISSIPPI

One method for compressing data is run length encoding (RLE).

When using RLE, the data in Figure 2 become:

1M 1I 2S 1I 2S 1I 2P 1I

Explain why RLE is not a suitable method for compressing the data in Figure 2.

Table 2 shows the Huffman codes for the characters used in the string PIEDPIPER

Table 2

Calculate how many bits would be saved if the phrase PIEDPIPER was encoded using the Huffman codes shown in Table 2, rather than using ASCII.

You should show your working.