Applied physics iii lecture3 digital_codes
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Applied physics iii lecture3 digital_codes
- 1. Applied physics III Digital Codes by Benson Mbuya
- 2. Binary Coded Decimal (BCD) • One of the most widely used representations of numerical data is the binary coded decimal (BCD) form in which each integer of a decimal number is represented by a 4-bit binary number (see conversion table). • It is particularly useful for the driving of display devices where a decimal output is desired. BCD usually refers to such coding in which the binary digits have their normal values, i.e., 8421. Sometimes it is written "8421 BCD" to clearly distinguish it from other binary codes such as the4221 Code, but when BCD is used without qualification, the 8421 version is assumed.
- 3. Binary Coded Decimal (BCD)
- 4. Binary-Coded Decimal (BCD) • Four bits per digit Digit Bit pattern 0 0000 Note: the following bit patterns are not used: 1 0001 2 0010 1010 1011 1100 1101 1110 1111 3 0011 4 0100 5 0101 6 0110 7 0111 8 1000 9 1001
- 5. Example • 709310 = ? (in BCD) 7 0 9 3 0111 0000 1001 0011
- 6. BCD
- 7. BCD Addition • Multi-digit BCD numbers can be added together 23 0010 0011 45 0100 0101 68 0110 1000 23 0010 0011 48 0100 1000 71 0110 1011 • 1011 is illegal BCD number
- 8. BCD Addition • Add a 0110 (6) to an invalid BCD number • Carry added to the most significant BCD digit 23 48 71 0010 0011 0100 1000 0110 1011 0110 0111 0001
- 9. 32 84 71 0011 0010 1000 0100 1011 0110 0110 10001 0110
- 10. Gray Code : Minimum Change code • Gray code is also known as reflected binary code. • The reflected binary code was originally designed to prevent spurious outputs from electromechanical switches. • Today, Gray codes are widely used to facilitate error correction in digital communications
- 11. Gray code
- 13. Converting Gray coded number to binary
- 16. Example: binary to gray code
- 17. Example: Gray code to Binary
- 18. Alphanumeric Codes • Represent numbers and alphabetic characters. —Also represent other characters such as symbols and various instructions necessary for conveying information. • The ASCII is the most common alphanumeric code. —ASCII = American Standard Code for Information Interchange
- 19. The Problem • Representing text strings, such as “Hello, world”, in a computer
- 20. Codes and Characters • Each character is coded as a byte • Most common coding system is ASCII (Pronounced ass-key) • ASCII = American National Standard Code for Information Interchange • Defined in ANSI document X3.4-1977
- 21. ASCII Features • • • • 7-bit code 8th bit is unused (or used for a parity bit) 27 = 128 codes Two general types of codes: —95 are “Graphic” codes (displayable on a console) —33 are “Control” codes (control features of the console or communications channel)
- 24. 000 001 0000 NULL DLE 0001 SOH DC1 0010 STX DC2 0011 ETX DC3 0100 EDT DC4 0101 ENQ NAK 0110 ACK SYN 0111 BEL ETB 1000 BS CAN 1001 HT EM 1010 LF SUB 1011 VT Least significantESC bit 1100 FF FS 1101 CR GS 1110 SO RS 1111 SI US 010 011 0 ! 1 " 2 # 3 Most significant bit $ 4 % 5 & 6 ' 7 ( 8 ) 9 * : + ; , < = . > / ? 100 @ A B C D E F G H I J K L M N O 101 P Q R S T U V W X Y Z [ ] ^ _ 110 ` a b c d e f g h i j k l m n o 111 p q r s t u v w x y z { | } ~ DEL
- 25. e.g., ‘a’ = 1100001 0000 0001 0010 0011 0100 0101 0110 0111 1000 1001 1010 1011 1100 1101 1110 1111 000 NULL SOH STX ETX EDT ENQ ACK BEL BS HT LF VT FF CR SO SI 001 DLE DC1 DC2 DC3 DC4 NAK SYN ETB CAN EM SUB ESC FS GS RS US 010 ! " # $ % & ' ( ) * + , . / 011 0 1 2 3 4 5 6 7 8 9 : ; < = > ? 100 @ A B C D E F G H I J K L M N O 101 P Q R S T U V W X Y Z [ ] ^ _ 110 ` a b c d e f g h i j k l m n o 111 p q r s t u v w x y z { | } ~ DEL
- 29. Extended ASCII • There are an additional 128 characters that were adopted by IBM for use in their PCs. It’s popular and is used in applications other than PCs unofficial standard. —The extended ASCII characters are represented by an 8-bit code series from 80h-FFh
- 31. Error Detection • Digital Systems are very Reliable • Errors during storage or transmission • Parity Bit —Even Parity —Odd Parity
- 35. Odd Parity Error Detection • • • • • • • • Original data 10011010 With Odd Parity 110011010 1-bit error 110111010 Number of 1s even indicates 1-bit error 2-bit error 110110010 Number of 1s odd no error indicated 3-bit error 100110010 Number of 1s even indicates error
- 36. BCD Addition • Try these: ex: Add the following numbers (a) (b) (c) (d) (e) (f) (g) (h) 0011+0100 00100011 + 00010101 10000110 + 00010011 010001010000 + 010000010111 1001 + 0100 1001 + 1001 00010110 + 00010101 01100111 + 01010011
- 38. references • http://hyperphysics.phyastr.gsu.edu/hbase/electronic/number3.html • http://hyperphysics.phyastr.gsu.edu/hbase/electronic/number3.html#c3 • http://autonopedia.org/crafts_and_technology/E lectronics/DigitalBasics/codes.html