Fundamentals of data representation

Convert the binary number 11010100 into decimal.

Convert the binary number 10111001 into hexadecimal. You should show your working.

State the largest decimal number that can be represented using 6 bits.

Add together the following three binary numbers and give your answer in binary. 00110110 10010010 + 00100001 ----------

Apply a binary shift three places to the right on the bit pattern 10101000. Give the result using 8 bits.

The arithmetic effect of applying a left binary shift of two to a binary number is to multiply that number by four. State the arithmetic effect of applying a left binary shift of four to a binary number.

State the arithmetic effect of applying a left binary shift of three followed by a right binary shift of five to a binary number.

How many bits are there in two kilobytes? Show your working.

The ASCII value for the character **x** is the decimal number 120. Complete **Table 1** with the missing ASCII and Unicode values.

**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. Define the term **sample resolution**.

State **one** disadvantage of a high sample resolution.

A 50-second sound has been recorded at a sample rate of 40 000 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.

State **two** reasons why data are compressed.

**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**.

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