1 / 136

EKT 121 / 4 ELEKTRONIK DIGIT 1

CHAPTER 1 : INTRODUCTION. EKT 121 / 4 ELEKTRONIK DIGIT 1. Lecturer : FAIRUL AFZAL Office : KKF 8 ( 04-9854150) Email :fairul@unimap.edu.my. Digital vs. analog quantities Decimal numbering system (Base 10) Binary numbering system (Base 2)

melia
Download Presentation

EKT 121 / 4 ELEKTRONIK DIGIT 1

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. CHAPTER 1 : INTRODUCTION EKT 121 / 4ELEKTRONIK DIGIT 1 Lecturer : FAIRUL AFZAL Office : KKF 8 (04-9854150) Email :fairul@unimap.edu.my

  2. Digital vs. analog quantities • Decimal numbering system (Base 10) • Binary numbering system (Base 2) • Hexadecimal numbering system (Base 16) • Octal numbering system (Base 8) • Number conversion • Binary arithmetic • 1’s and 2’s complements of binary numbers 1.0 Number & codes

  3. Signed numbers • Arithmetic operations with signed numbers • Binary-Coded-Decimal (BCD) • ASCII codes • Gray codes • Digital codes & parity Number & codes

  4. Digital vs. Analogue • Digital signals are represented by only two possible - • 1 (binary 1) 0r 0 (binary 0) • Sometimes call these values “high” and “low” or “ true” and “false”” • Example : light switch , it can be in just two position – “ on ” or “ off ” • More complicated signals can be constructed from 1s and 0s by stringing them end-to end. Example : 3 binary digits, have 8 possible combinations : • 000,001,010,011,100,101,110 and 111. • The diagram : example a typical digital signal, represented as a series of voltage levels that change as time goes on.

  5. Digital vs. Analogue • Analogue electronics can be any value within limits. • Example : Voltage change simultaneously from one value to the next, like gradually turning a light dimmer switch up or down. • The diagram below shows an analoq signal that changes with time.

  6. Why digital ? • Problem with all signals – noise • Noise isn't just something that you can hear - the fuzz that appears on old video recordings also qualifies as noise. In general, noise is any unwanted change to a signal that tends to corrupt it. • Digital and analogue signals with added noise: Digital vs. Analogue Analog : never get back a perfect copy of the original signal Digital : easily be recognized even among all that noise : either 0 or 1

  7. Two ways of representing the numerical values of quantities : i) Analog (continuous) ii) Digital (discrete) Analog : a quantity represented by voltage, current or meter movement that is proportional to the value that quantity • Digital : the quantities are represented not by proportional quantities but by symbols called digits Digital and analog quantities

  8. Digital system: • combination of devices designed to manipulate logical information or physical quantities that are represented in digital forms • Example : digital computers and calculators, digital audio/video equipments, telephone system. • Analog system: • contains devices manipulate physical quantities that are represented in analog form • Example : audio amplifiers, magnetic tape recording and playback equipment, and simple light dimmer switch Digital and analog systems

  9. Analog Quantities • Continuous values

  10. Digital Waveform

  11. We are all familiar with decimal number systems - use everyday :calculator, calendar, phone or any common devices use this numbering system : Decimal = Base 10 • Some other number systems: • Binary = Base 2 • Octal = Base 8 • Hexadecimal = Base 16 Introduction to Numbering Systems

  12. 0 ~ 9 • 0 ~ 1 • 0 ~ 7 • 0 ~ F Numbering Systems • Decimal • Binary • Octal • Hexadecimal

  13. Dec Hex Octal Binary 0123456789101112131415 0123456789ABCDEF 000001002003004005006007010011012013014015016017 00000000000000010000001000000011000001000000010100000110000001110000100000001001000010100000101100001100000011010000111000001111 N U M B E R S Y S T E M S

  14. Binary: 11101101 Most significant digit Least significant digit Hexadecimal: 1D63A7A Most significant digit Least significant digit Significant Digits

  15. Base 10 - (0,1,2,3,4,5,6,7,8,9) • Example : 39710 3 9 7 Decimal numbering system (Base 10) Weights for whole numbers are positive power of ten that increase from right to left , beginning with 100 + 7 X 100 3 X 102 9 X 101 + = 300 + 90 + 7 39710 =

  16. Base 2 system – (0 , 1) • used to model the series of electrical signals computers use to represent information • 0 represents the no voltage or an off state • 1 represents the presence of voltage or an on state • Example : 1012 1 0 1 Binary Number System Weights in a binary number are based on power of two, that increase from right to right to left,beginning with 20 + 0 X 21 + 1 X 20 1X 22 = 4 + 0 + 1 = 510

  17. Base 8 system – (0,1,2,3,4,5,6,7) • multiplication and division algorithms for conversion to and from base 10 • Example : 7568 convert to decimal: 7 5 6 Octal Number System Weights in a binary number are based on power of eight that increase from right to right to left,beginning with 80 + 7X 82 5 X 81 + 6 X 80 = 448 + 40 + 6 49410 = • Readily converts to binary • Groups of three (binary) digits can be used to represent each octal number • Example : 7568 convert to binary : • 7 5 68 1111011102

  18. Base 16 system • Uses digits 0 ~ 9 & letters A,B,C,D,E,F • Groups of four bitsrepresent eachbase 16 digit Hexadecimal Number System

  19. Base 16 system – • multiplication and division algorithms for conversion to and from base 10 • Example : A9F16 convert to decimal: A 9 F Hexadecimal Number System Weights in a hexadecimal number are based on power of sixteen that increase from right to right to left,beginning with 160 10X 162 9 X 161 + 15 X 160 + = 2560 + 144 + 15 271910 = • Readily converts to binary • Groups of four (binary) digits can be used to represent each hexadecimal number • Example : A9F8 convert to binary : • A 9 F16 1010100111112

  20. Number Conversion • Any Radix (base) to Decimal Conversion

  21. Number Conversion (BASE 2 –BASE 10) • Binary to Decimal Conversion

  22. Convert (10101101)2 to its decimal equivalent: Binary 1 0 1 0 1 1 0 1 Positional Values Binary to Decimal Conversion x x x x x x x x 27 26 25 24 23 22 21 20 128 + 32 + 8 + 4 + 1 Products 17310

  23. Convert 6538 to its decimal equivalent: Octal to Decimal Conversion Octal Digits 6 5 3 x x x Positional Values 82 81 80 Products 384 + 40 + 3 42710

  24. Convert 3B4F16 to its decimal equivalent: Hex Digits Hexadecimal to Decimal Conversion 3 B 4 F x x x x Positional Values 163 162 161 160 12288 +2816 +64 +15 Products 15,18310

  25. Number Conversion • Decimal to Any Radix (Base) Conversion • INTEGER DIGIT: Repeated division by the radix & record the remainder • FRACTIONAL DECIMAL: Multiply the number by the radix until the answer is in integer Example: 25.3125 to Binary

  26. Decimal to Binary Conversion Remainder 2 5 = 12 + 1 2 1 2 = 6 + 0 2 6 = 3 + 0 2 3 = 1 + 1 2 1 = 0 + 1 2 MSB LSB 2510 = 1 1 0 0 1 2

  27. Decimal to Binary Conversion MSB LSB Carry . 0 1 0 1 0.3125 x 2 = 0.625 0 0.625 x 2 = 1.25 1 0.25 x 2 = 0.50 0 0.5 x 2 = 1.00 1 The Answer: 1 1 0 0 1.0 1 0 1

  28. Convert 42710 to its octal equivalent: 427 / 8 = 53 R3 Divide by 8; R is LSD 53 / 8 = 6 R5 Divide Q by 8; R is next digit 6 / 8 = 0 R6 Repeat until Q = 0 Decimal to Octal Conversion 6538

  29. Convert 83010 to its hexadecimal equivalent: 830 / 16 = 51 R14 51 / 16 = 3 R3 3 / 16 = 0 R3 Decimal to Hexadecimal Conversion = E in Hex 33E16

  30. Number Conversion • Binary to Octal Conversion (vice versa) • Grouping the binary position in groups of three starting at the least significant position.

  31. Each octal number converts to 3 binary digits Octal to Binary Conversion To convert 6538 to binary, just substitute code: 6 5 3 110 101 011

  32. Number Conversion • Example: • Convert the following binary numbers to their octal equivalent (vice versa). • 1001.11112 b) 47.38 • 1010011.110112 • Answer: • 11.748 • 100111.0112 • 123.668

  33. Number Conversion • Binary to Hexadecimal Conversion (vice versa) • Grouping the binary position in 4-bit groups, starting from the least significant position.

  34. The easiest method for converting binary to hexadecimal is to use a substitution code Each hex number converts to 4 binary digits Binary to Hexadecimal Conversion

  35. Number Conversion • Example: • Convert the following binary numbers to their hexadecimal equivalent (vice versa). • 10000.12 • 1F.C16 • Answer: • 10.816 • 00011111.11002

  36. Convert 0101011010101110011010102 to hex using the 4-bit substitution code : 0101 0110 1010 1110 0110 1010 Substitution Code 5 6 A E 6 A 56AE6A16

  37. Substitution code can also be used to convert binary to octal by using 3-bit groupings: 010 101 101 010 111 001 101 010 Substitution Code 2 5 5 2 7 1 5 2 255271528

  38. Binary Addition 0 + 0 = 0 Sum of 0 with a carry of 0 0 + 1 = 1 Sum of 1 with a carry of 0 1 + 0 = 1 Sum of 1 with a carry of 0 1 + 1 = 10 Sum of 0 with a carry of 1 Example: 11001 111 + 1101 + 11 100110 ???

  39. Simple Arithmetic • Example: 5816 + 2416 7C16 • Addition • Example: 100011002 + 1011102 101110102 • Substraction • Example: 10001002 - 1011102 101102

  40. Binary Subtraction 0 - 0 = 0 1 - 1 = 0 1 - 0 = 1 10 -1 = 1 0 -1 with a borrow of 1 Example: 1011 101 - 111 - 11 100 ???

  41. Binary Multiplication 0 X 0 = 0 0 X 1 = 0 Example: 1 X 0 = 0 100110 1 X 1 = 1 X 101 100110 000000 + 100110 10111110

  42. Binary Division Use the same procedure as decimal division

  43. Changing all the 1s to 0s and all the 0s to 1s Example: 1 1 0 1 0 0 1 0 1 Binary number 0 0 1 0 1 1 0 1 0 1’s complement 1’s complements of binary numbers

  44. 2’s complement • Step 1: Find 1’s complement of the number Binary # 11000110 1’s complement 00111001 • Step 2: Add 1 to the 1’s complement 00111001 + 00000001 00111010 2’s complements of binary numbers

  45. Signed Magnitude Numbers 110010.. …00101110010101 Sign bit 31 bits for magnitude 0 = positive 1 = negative This is your basic Integer format

  46. Left most is the sign bit • 0 is for positive, and 1 is for negative • Sign-magnitude • 0 0 0 1 1 0 0 1 = +25 sign bit magnitude bits • 1’s complement • The negative number is the 1’s complement of the corresponding positive number • Example: +25 is 00011001 -25 is 11100110 Sign numbers

  47. 2’s complement • The positive number – same as sign magnitude and 1’s complement • The negative number is the 2’s complement of the corresponding positive number. Example Express +19 and -19 in i. sign magnitude ii. 1’s complement iii. 2’s complement Sign numbers

  48. Digital Codes • BCD (Binary Coded Decimal) Code • Represent each of the 10 decimal digits (0~9) as a 4-bit binary code. • Example: • Convert 15 to BCD. 1 5 0001 0101BCD • Convert 10 to binary and BCD.

  49. Digital Codes • ASCII (American Standard Code for Information Interchange) Code • Used to translate from the keyboard characters to computer language Can convert from ASCII code to binary / hexadecimal/ or any numbering systems and vice versa How to convert ?????

  50. Digital Codes • The Gray Code • Only 1 bit changes • Can’t be used in arithmetic circuits • Can convert from Binary to Gray Code and vice versa. • How to convert ?????

More Related