Chapter 2 Data Representation.

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1 Chapter 2 Data Representation

2 OBJECTIVES After reading this chapter, the reader should be able to:
Define data types. Visualize how data are stored inside a computer. Understand the differences between text, numbers, images, video, and audio. Work with hexadecimal and octal notations.

3 2.1 DATA TYPES

4 Different types of data
Figure 2-1 Different types of data

5 Note: The computer industry uses the term “multimedia” to define information that contains numbers, text, images, audio, and video.

6 2.2 DATA INSIDE THE COMPUTER

7 Figure 2-2 Bit pattern

8 Examples of bit patterns
Figure 2-3 Examples of bit patterns

9 2.3 REPRESENTING DATA

10 Representing symbols using bit patterns
Figure 2-4 Representing symbols using bit patterns

11 Table 2.1 Number of symbols and bit pattern length
4 8 16 … 128 256 65,536 Bit Pattern Length 1 2 3 4 … 7 8 16

12 Representation of the word
Figure 2-5 Representation of the word “BYTE” in ASCII code

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14 Unicode 16 bits e.g. 趙(8D99) 坤(5764) 茂(8302)

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18 Image representation methods
Figure 2-6 Image representation methods

19 Bitmap graphic method of a black-and-white image
Figure 2-7 Bitmap graphic method of a black-and-white image

20 Representation of color pixels
Figure 2-8 Representation of color pixels

21 Figure 2-9 Audio representation

22 2.4 HEXADECIMAL NOTATION

23 Note: A 4-bit pattern can be represented by a hexadecimal digit, and vice versa.

24 Table 2.2 Hexadecimal digits
Bit Pattern 0000 0001 0010 0011 0100 0101 0110 0111 Hex Digit 1 2 3 4 5 6 7 Bit Pattern 1000 1001 1010 1011 1100 1101 1110 1111 Hex Digit 8 9 A B C D E F

25 Binary to hexadecimal and hexadecimal to binary transformation
Figure 2-10 Binary to hexadecimal and hexadecimal to binary transformation

26 Example 1 Show the hexadecimal equivalent of the bit pattern Solution Each group of 4 bits is translated to one hexadecimal digit. The equivalent is xCE2.

27 Show the hexadecimal equivalent of the bit pattern 0011100010.
Example 2 Show the hexadecimal equivalent of the bit pattern Solution Divide the bit pattern into 4-bit groups (from the right). In this case, add two extra 0s at the left to make the number of bits divisible by 4. So you have , which is translated to x0E2.

28 Example 3 What is the bit pattern for x24C? Solution Write each hexadecimal digit as its equivalent bit pattern to get

29 2.5 OCTAL NOTATION

30 A 3-bit pattern can be represented by an octal digit, and vice versa.
Note: A 3-bit pattern can be represented by an octal digit, and vice versa.

31 Table Octal digits Bit Pattern 000 001 010 011 Oct Digit 1 2 3 Bit Pattern 100 101 110 111 Oct Digit 4 5 6 7

32 Binary to octal and octal to binary transformation
Figure 2-11 Binary to octal and octal to binary transformation

33 Example 4 Show the octal equivalent of the bit pattern Solution Each group of 3 bits is translated to one octal digit. The equivalent is 0562, o562, or 5628.

34 Show the octal equivalent of the bit pattern 1100010.
Example 5 Show the octal equivalent of the bit pattern Solution Divide the bit pattern into 3-bit groups (from the right). In this case, add two extra 0s at the left to make the number of bits divisible by 3. So you have , which is translated to 1428.

35 Write each octal digit as its equivalent bit pattern to get 010100.
Example 6 What is the bit pattern for 248? Solution Write each octal digit as its equivalent bit pattern to get

36 一個小小的問題 Oct-這個字根代表8; Dec-這個字根代表10，為什麼October 不是八月而是十月？為什麼 December不是十月而是十二月？

37 因為插入了七月和八月 July源於凱撒(Julius Caesar) 之名，凱撒原是一位有名的羅馬將領，後來當了羅馬皇帝。在這之前就有曆法，那時是以March 為一年的開端，而July是第十五個月；到了凱撒當皇帝便修改曆法，將一年的開始訂為January，而將July 提升到第七位，這個改變一直沿用至今。 凱撒大帝之後，他的兒子奧古斯都(Augustus)繼承王位，人們尊稱他為Augustus，其意義乃代表高貴 (Noble)，於是他學凱撒將他的幸運月，以自己的封號命名，並從二月挪一天過來，變成三十一日。 那二月為什麼只有二十八天呢？

38 二月被砍過兩天 二月為什麼通常只有二十八天？
凱撒(Julius Caesar) 修改曆法時，本來規定每年十二個月裡，逢單是大月三十一日，逢雙是小月三十日，但是這樣算下來，一年就變成三百六十六日，所以必須設法在一年中扣去一天。那時候判處死刑的人犯均在二月分執行，因此人們認為二月是不吉利的月分，既然要扣除一天，那麼就由二月分來扣掉，讓不吉利的日子減少一天，因此二月分就成了二十九日。 後來奧古斯都(Augustus)繼凱撒之後當了羅馬皇帝，他發現凱撒是七月生的，而七月是逢單為大月三十一日；他不服氣，為了表示自己也偉大，就把自己八月出生的月分改為大月三十一日。糟了又多出一天怎麼辦？那還是由二月分來扣除，因此結果二月分就變成二十八日。