LectureSlides1001 Data Storage.ppt [相容模式]

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1 (continued) 1.6 Storing Integers 1.7 Storing Fractions 1.8 Data Compression 1.9 Communications Errors Bits and Their Storage 1.2 Main Memory 1.3 Mass Storage 1.4 Representing Information as Bit Patterns 1.5 The Binary System Bit ( 位元 ): Binary Digit ( 二進位數字 0 or 1) Bit Patterns are used to represent information. Numbers Text characters Images Sound And others

2 Boolean Operation( 布林運算 ): An operation that manipulates one or more true/false values Specific operations AND ( 且 ) OR ( 或 ) XOR (exclusive or) ( 互斥或 ) NOT ( 非 ) Gate ( 邏輯閘 ): A device that computes a Boolean operation Often implemented as (small) electronic circuits Provide the building blocks from which computers are constructed Figure 1.1 The Boolean operations AND, OR, and XOR (exclusive or) Figure 1.2 A pictorial representation of AND, OR, XOR, and NOT gates as well as their input and output values

3 Flip-flop ( 正反器 ): A circuit built from gates that can store one bit. Has an input line which sets its stored value to 1 Has an input line which sets its stored value to 0 While both input lines are 0, the most recently stored value is preserved Figure 1.3 A simple flip-flop circuit

4 Hexadecimal notation(16 進位表示法 ): A shorthand notation for long bit patterns Divides a pattern into groups of four bits each Represents each group by a single symbol Example: becomes A

5 Cell ( 記憶單元 ): A unit of main memory (typically 8 bits which is one byte ( 位元組 )) Most significant bit: the bit at the left (high-order) end of the conceptual row of bits in a memory cell Least significant bit: the bit at the right (low-order) end of the conceptual ceptua row of bits in a memory cell Address( 位址 ): A name that uniquely identifies one cell in the computer s main memory The names are actually numbers. These numbers are assigned consecutively starting at zero. Numbering the cells in this manner associates an order with the memory cells

6 Random Access Memory (RAM): Memory in which individual cells can be easily accessed in any order ( 隨機存取記憶體 ) Dynamic Memory (DRAM): RAM composed of volatile memory ( 動態記憶體 ) On-line versus off-line Typically larger than main memory Typically less volatile than main memory Typically slower than main memory Kilobyte: 2 10 bytes = 1024 bytes Example: 3 KB = bytes Sometimes kibi rather than kilo Megabyte: 2 20 bytes = 1,048,576 bytes Example: 3 MB = 3 1,048,576, bytes Sometimes megi rather than mega Gigabyte: 2 30 bytes = 1,073,741, bytes Example: 3 GB = 3 1,073,741,824 bytes Sometimes gigi rather than giga Magnetic Systems Disk Tape Optical Systems CD DVD Flash Drives

7 File( 檔案 ): A unit of data stored in mass storage system Fields and keyfields Physical record versus Logical record (See the figure on the next page) Buffer( 緩衝記憶區 ): A memory area used for the temporary storage of data (usually as a step in transferring the data)

8 Each character (letter, punctuation, etc.) is assigned a unique bit pattern. ASCII: Uses patterns of 7-bits to represent most symbols used in written English text Unicode: Uses patterns of 16-bits to represent the major symbols s used in languages world side ISO standard: Uses patterns of 32-bits to represent most symbols used in languages world wide Binary notation( 二進位表示法 ): Uses bits to represent a number in base two Limitations it ti of computer representations ti of numeric values Overflow happens when a value is too big to be represented Truncation happens when a value is between two representable values

9 Figure 1.14 The sound wave represented by the sequence 0, 1.5, 2.0, 1.5, 2.0, 3.0, 4.0, 3.0, 0 Bit map techniques Pixel: short for picture element RGB Luminance and chrominance Vector techniques Scalable TrueType and PostScript Sampling techniques Used for high quality recordings Records actual audio MIDI Used in music synthesizers Records musical score The traditional decimal system is based on powers of ten. The Binary system is based on powers of two

10 Figure 1.17 An algorithm for finding the binary representation of a positive integer Figure 1.18 Applying the algorithm in Figure to obtain the binary representation of thirteen

11 Two s complement notation ( 二的補數表示法 ) : The most popular means of representing integer values Excess notation ( 超額表示法 ) : Another means of representing integer values Both can suffer from overflow errors

12 Figure 1.22 Coding the value -6 in two s complement notation using four bits Figure 1.23 Addition problems converted to two s complement notation Figure 1.25 An excess notation system using bit patterns of length three

13 Floating-point Notation: Consists of a sign bit, a mantissa field, and an exponent field. Rltdt Related topics include ld Normalized form Truncation errors Lossy versus lossless Run-length encoding Frequency-dependent encoding 正負號 指數 假數 (Huffman codes) Relative encoding Dictionary encoding (Includes adaptive dictionary i encoding such as LZW encoding.)

14 GIF: Good for cartoons JPEG: Good for photographs TIFF: Good for image archiving Parity bits (even versus odd) Checkbytes Error correcting codes Figure 1.28 The ASCII codes for the letters A and F adjusted for odd parity MPEG High definition television broadcast Video conferencing MP3 Temporal masking Frequency masking

15 補充 漢明碼, 錯誤更正碼 於原資料的資料位元中插入同位元, 若有 n 個資料位元, 則須插入 k 個同位元, 形成 n+k 個位元,n 與 k 應滿足 : 2 k n+k+1 插入之同位元應置於 2 0,2 1,2 2, 的位元位置, 若原始資料為 D 0 D 1 D 2 D 3, 插入同位元後的漢明碼為 : D 3 D 2 D 1 P 4 D 0 P 2 P 1 P 7 P 6 P 5 P 4 P 3 P 2 P Figure 1.30 Decoding the pattern using the code in Figure 1.30 編碼規則與錯誤校正方式 插入之同位元 (P 1 P 2 P 4 ) 須滿足下列偶同位公式 : P 1 P 3 P 5 P 7 =0 P 2 P 3 P 6 P 7 =00 P 4 P 5 P 6 P 7 =0 錯誤校正方式 : 當接收到 P 7 P 6 P 5 P 4 P 3 P 2 P 1 時, 以下列公式求出 C 1 C 2 C 3 : C 1 =P 1 P 3 P 5 P 7 C 2 =P 2 P 3 P 6 P 7 C 3 =P 4 P 5 P 6 P

16 錯誤校正方式 若 C 1 =1, 則在位元 P 1 P 3 P 5 P 7 中, 有一位元錯誤若 C 2 =1, 則在位元 P 2 P 3,P 6 P 7 中, 有一位元錯誤若 C 3 =1, 則在位元 P 4 P 5 P 6 P 7 中, 有一位元錯誤 C 3 C 2 C 1 代表意義 所接收到的 P 7 P 6 P 5 P 4 P 3 P 2 P 1 資料正確無誤 P 1 位元錯誤 P 2 位元錯誤 P 3 位元錯誤 P 4 位元錯誤 P 5 位元錯誤 P 6位元錯誤 P 7 位元錯誤 1-61 漢明距離 ( ) 兩組位元串中, 相對應位置之資料 ( 位元值 0 或 1) 有多少個不一樣示例 : 漢明距離為 2 漢明距離為 4 代碼 ( 碼集合 ) 之漢明距離 : 算出各碼值彼此間之漢明距離, 取其最小者為整個代碼之漢明距離 整個代碼之漢明距離 : 可偵查錯誤之位元數目可校正之位元數目