A3. Data Representation

Learning Outcomes:

Distinguish between analog and digital data. State applications or situations where conversion of analog to digital data is required, or vice versa.
Explain why IT uses digital data

The relationship between the number of bits and number of patterns/combinations available should be mentioned (e.g. three bits can be used to represent eight colours).

Convert integers from denary numbers to binary numbers or hexadecimal numbers, or vice versa.
Adopt two’s complement for the representation of negative integers.
Perform simple calculations (addition and subtraction only) on binary numbers and analyse overflow errors.

In understanding errors, minimum and maximum numbers an n-bit can hold (maximum 2 bytes) should be considered.

Know how characters are represented by using common international standards such as American Standard Code for Information Interchange (ASCII), the Big-5 code, the Guobiao (GB) code and the Unicode.

The relationship between the size of the character set and the representation should be explained. Recall of specific codes is not required.

Know briefly how different multimedia elements are digitised. Convert them into different file formats and compare them for storing the same data.

Elementary file conversion is required but not the editing of a file. Students should be given the experience in creating various file formats such as wav vs. mp3, bmp vs. jpg, and avi vs. mpeg2.

Bits vs combinations

No. of bits	Possible combinations	Calculation of combinations
1 bit	0,1	2¹=2
2 bits	00,01,10,11	2²=4
…	…	…
n bits		2ⁿ

Representation of negative integers

Use 2’s complement method in modern computer

Suppose we use 4 bits to represent number: first bit is the sign (+/-) and remaining bits are the size

For 0 and positive numbers, the sign bit is 0

For negative numbers, we can derive the binary form from the positive number using 2’s complement method

-1:

So, the range of numbers represented by 4 bits is -2³ to 2³-1.

I.e. the range of numbers represented by n bits is -2^n-1to 2^n-1-1

Overflow errors

For 2 numbers with different signs, their sum will not overflow.
If the 2 numbers have same signs, overflow may happen. i.e. when the result has different sign bit, overflow has occurred.

Character representation

ASCII (American Standard Code for Information Interchange), 7 bits for each character
Big-5 code: Traditional Chinese, 2 bytes for each character
GB (Guobiao) Code: Simplified Chinese, 2 bytes for each character
Unicode: Characters of different languages (If you need to use traditional and simplified Chinese at the same time, use Unicode), 1 to 4 bytes for each character

Multimedia elements

File size depends on:

BMP: Bitmap. Uncompressed format à large file size
JPEG: Joint Photographic Experts Group. Lossy compression à small file size, commonly used in the internet and supported by most browsers
GIF: Graphics Interchange Formats. Supports animation and transparency. 256 colours only à not good for photos
PNG: Portable Network Graphics. Lossless compression à file size bigger than JPEG. Support more colour than GIF à better image quality than GIF