Unit 3. Digital encoding

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1 Unit 3. Digital encoding Digital Electronic Circuits (Circuitos Electrónicos Digitales) E.T.S.I. Informática Universidad de Sevilla 9/2012 Jorge Juan 2010, 2011, 2012 You are free to copy, distribute and communicate this work publicly and make derivative work provided you cite the source and respect the conditions of the Attribution-Share alike license from Creative Commons. You can read the complete license at: Contents Digital encoding Digital units Binary numbers Octal and hexadecimal Fractions Binary codes

2 Digital encoding Text Audio 5, 17, 31, Image Computer Video Digital units BIT (b) (BInary digit) Simbol in the set {0,1} Minimum information unit Word Set of 'n' bits, typically 8, 16, 32 or 64. Computers work with a whole word at a time Byte (B) 8 bit word Basic practical information unit

3 Digital units Tradition: IS units with slightly changed meaning (powers of 2 instead of 10) Non-uniform use of digital units: Diskette: 1.44MB = 1000 KB = 1000x1024B Disc 160GB = MB = 160x1000x1024x1024B DVD 4,7GB = 4700MB = 4,7x1000x1024x1024B There is a (not very used) standard for binary units: IEC, IEEE SI Binary IEC kilo k kibi Ki mega M mebi Mi giga G gibi Gi tera T tebi Ti peta P pebi Pi exa E exbi Ei zetta Z zebi Zi Binary numbers. Positional notation Decimal system: 10 symbols {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} Base = Weight: Symbol: Value:

4 Binary numbers. Positional notation Binary system: 2 symbols {0,1} Base = Weight: Symbol: Value: Binary numbers. Positional notation In general Magnitude x Base b n figures: {x i } x=x n 1 b n 1... x 1 b 1 x 0 b 0 Maximum representable number: b n -1

5 Base 'b' to base '10' conversion Simply by applying the formula Ej: 234 (7 x=x n 1 b n 1... x 1 b 1 x 0 b 0 Base '10' to base 'b' conversion Successive division by the target base Successive reminders are the base-n figures from less significant to most significant 123 ( (

6 Octal and hexadecimal Base 8 (octal): {0, 1, 2, 3, 4, 5, 6, 7} Base 16 (hexadecimal): {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F} Compact way to represent binary numbers 1 octal figure = 3 binary figures 1 hexadecimal figure = 4 binary figures Octal and hexadecimal B-8 B B-10 B-16 B A B C D E F 1111

7 Octal and hexadecimal ( B A 2BA (16 2BA (16 = 2BA h = 2BA hex = #2BA = $2BA = 0x2BA = 10'h2BA Binary numbers. Fractions x=x n 1 b n 1... x 0 b 0 x 1 b 1... x m b m integer part fractional part

8 Binary numbers. Fractions Base b to base 10 conversion Directly: just operate in base ,101 2 = /2 1/8=2, Base 10 to base b: Integer part: like integer numbers Fractional part: successive multiplication by the target base. Take the integer part of the result. Binary numbers. Fractions Example: 3,27 (10 3 (10 = 11 (2 0,27 x 2 = 0,54 -> "0" 0,54 x 2 = 1,08 -> "1" 0,08 x 2 = 0,16 -> "0" 0,16 x 2 = 0,32 -> "0" 0,32 x 2 = 0,64 -> "0" 0,64 x 2 = 1,28 -> "1"... 3,27 (10 11, (2

9 Binary codes Assignment of binary values to a set of symbols Numbers, characters, colors, Usually, fixed width words (e.g. 8 bits) but not always Code assignment seeks good properties Similar codes for similar colors Similar codes for lower and upper-case letters Some times, not all binary words have a corresponding symbol assigned Natural binary Natural integer coding using base-2 binary numbers Number Code

10 Gray code Code positive integers Number 1 bit 2 bits 3 bits 4 bits Consecutive symbols only differ in one bit (distance 1) The n-bit code is built by reflecting the n-1-bit code One-hot code Number Code Code words with only one bit set to '1' Pros: Easy to decode Allow for error detection Cons: Number of bits = number of symbols to code

11 BCD codes (Binary Coding Decimal) Binary coding of base-10 figures 7 segm. Fig. natural excess out-of-5 abcdefg a f g e d b c Parity bit The parity of a binary word is even / odd if the number of bits set to 1 is even/odd. Parity bit: additional bit added to a code to achieve a determined parity, even or odd E.g. natural binary code with even leading parity bit. Number Code

12 Text encoding Binary encoding of text symbols or 'characters'. Include graphical and control symbols: new line, tab, end of file,... There are many text encodings around for historical and technical reasons Text encoding ASCII (American Standard Code for Information Interchange) (ISO-646-IRV) 7-bit (128 symbols), very popular, covers basically the English language. ISO (Latin 1) 8-bit (256 symbols) ASCII extension for Western Europe languages. ISO (Latin 9) Latin 1 update (Euro symbol and others). ISO a ISO Other ASCII extensions: Cyrillic, Arab, Greek, Hebrew,... ISO (Unicode) 16-bit universal encoding.

13 ACII 0 00 NUL SPC ` 1 01 SOH 33 21! A a 2 02 STX " B b 3 03 ETX # C c 4 04 EOT $ D d 5 05 ENQ % E e 6 06 ACK & F f 7 07 BEL ' G g 8 08 BS ( H h 9 09 HT ) I i 10 0A LF 42 2A * 74 4A J 106 6A j 11 0B VT 43 2B B K 107 6B k 12 0C FF 44 2C, 76 4C L 108 6C l 13 0D CR 45 2D D M 109 6D m 14 0E SO 46 2E. 78 4E N 110 6E n 15 0F SI 47 2F / 79 4F O 111 6F o DLE P p DC Q q DC R r DC S s DC T t NAK U u SYN V v ETB W w CAN X x EM Y y 26 1A SUB 58 3A : 90 5A Z 122 7A z 27 1B ESC 59 3B ; 91 5B [ 123 7B { 28 1C FS 60 3C < 92 5C \ 124 7C 29 1D GS 61 3D = 93 5D ] 125 7D } 30 1E RS 62 3E > 94 5E ^ 126 7E ~ 31 1F US 63 3F? 95 5F _ 127 7F DEL ISO (Latin 1) 160 A0 192 C0 À 224 E0 à 161 A1 193 C1 Á 225 E1 á 162 A2 194 C2 Â 226 E2 â 163 A3 195 C3 Ã 227 E3 ã 164 A4 196 C4 Ä 228 E4 ä 165 A5 197 C5 Å 229 E5 å 166 A6 198 C6 Æ 230 E6 æ 167 A7 199 C7 Ç 231 E7 ç 168 A8 200 C8 È 232 E8 è 169 A9 201 C9 É 233 E9 é 170 AA ª 202 CA Ê 234 EA ê 171 AB «203 CB Ë 235 EB ë 172 AC 204 CC Ì 236 EC ì 173 AD CD Í 237 ED í 174 AE 206 CE Î 238 EE î 175 AF 207 CF Ï 239 EF ï 176 B0 208 D0 Ð 240 F0 ð 177 B1 ± 209 D1 Ñ 241 F1 ñ 178 B2 ² 210 D2 Ò 242 F2 ò 179 B3 ³ 211 D3 Ó 243 F3 ó 180 B4 212 D4 Ô 244 F4 ô 181 B5 µ 213 D5 Õ 245 F5 õ 182 B6 214 D6 Ö 246 F6 ö 183 B7 215 D7 247 F7 184 B8 216 D8 Ø 248 F8 ø 185 B9 ¹ 217 D9 Ù 249 F9 ù 186 BA º 218 DA Ú 250 FA ú 187 BB» 219 DB Û 251 FB û 188 BC ¼ 220 DC Ü 252 FC ü 189 BD ½ 221 DD Ý 253 FD ý 190 BE ¾ 222 DE Þ 254 FE þ 191 BF 223 DF ß 255 FF ÿ

14 Graphics (image) pixel Red Green Blue ,172,44 Sound Quality parameters Sampling rate (e.g Hz) Bit resolution (e.g. 16 bits) Number of channels (e.g. 2 -stereo-)

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