Higher Computing – Computer Systems : Data Representation Homework
Homework 1 - Text Representation
1. Describe how ASCII is used to represent text. 1
2. Most modern computers use Unicode rather than ASCII to represent text. State one advantage of Unicode when compared to ASCII. 1
3. ASCII and UNICODE are both used to represent text in computer systems.
(a) Describe one advantage of UNICODE over ASCII. 1
(b) Describe one disadvantage of UNICODE over ASCII. 1
Homework 2 - Number Representation
1. One method of representing a negative integer in a computer is by using the two's complement of the corresponding positive integer. Which of the following is the 8 bit two's complement representation of -7?
(a) 00000111
(b) 10000111
(c) 11111001 1
2. Describe one way of storing a real number in computer memory. 1
3. What is the 8 bit two’s complement representation of the number --72? 1
4. In computer systems, integers are stored using two's complement representation. What would be the range of integers which could be stored in one byte if two's complement representation was used? 1
5. In computer systems, large numbers are stored using floating point representation. State the effect of increasing the number of bits used to store:
(i) the mantissa; (ii) the exponent. 2
6. Give two reasons why computers use binary numbers to represent and store data. 2
7. Which one of the following is the 8-bit two's complement representation of -14?
(a) 11110001
(b) 11110010
(c) 10001110
(d) 11110011 1
8. Write the binary number 1000100111 as a positive integer. 1
9. Represent the decimal number –73 using 8 bit two’s complement. 1
10. Convert this 8-bit two’s complement binary number into a decimal.
11010011 1
Homework 3 - Graphic Representation
1. A scanner is used to scan a 5 in by 7 in photograph at 600 dpi in 256 colours. How much memory would be required to store the scanned image? 2
2. The image in Figure 1 has been created using a graphics package.
Figure 1
Describe two ways in which this image could be represented in memory. 4
3. A scanned image measures 3 inches by 4 inches. It was scanned at 600 dpi in 256 colours. Calculate the storage requirements for the scanned image in megabytes. Show all your working. 2
4. Two versions of the image below have been created. One in a bit-mapped graphic package and the other in a vector graphic package.
If a circle is added to the centre of the graphic, what is the effect on the file size in each case? 2
5. John uses his digital camera to take photographs. It has a 512 Megabyte memory card. His camera uses 16,777,216 colours and is set to a resolution of 3000 × 2000 pixels.
(a) Calculate the file size of a single image. Your answer should be in appropriate units. Show all working. 3
(b) What is the maximum number of images of this size that can be stored on John’s memory card? 2
(c) He changes the setting in his camera to reduce the bit-depth.
Describe one effect that this will have. 1
6. State the number of bits required to represent 16 777 216 colours. 1
7. Carolyn reduces the bit-depth of photographs from 24 bits to 16 bits before saving them onto the hard disk of her computer.
(a) Describe one advantage of reducing the bit-depth of the photographs from 24 to
16. 2
(b) Describe one disadvantage of reducing the bit-depth of the photographs from 24
to 16. 2
(c) A 4 inch by 6 inch photograph with a resolution of 600 dpi and using 16-bit colour depth is stored. Calculate the file size of the photograph. State your answer using appropriate units. Show all your working. 3