1 / 55

EKT 121 / 3 ELEKTRONIK DIGIT 1

EKT 121 / 3 ELEKTRONIK DIGIT 1. CHAPTER 1 INTRODUCTION TO DIGITAL LOGIC. Number & codes (1). Digital vs. Analog Numbering systems Decimal (Base 10) Binary (Base 2) Hexadecimal ( Base 16) Octal ( Base 8) Number conversion Binary arithmetic

talli
Download Presentation

EKT 121 / 3 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. EKT 121 / 3ELEKTRONIK DIGIT 1 CHAPTER 1 INTRODUCTION TO DIGITAL LOGIC

  2. Number & codes (1) • Digital vs. Analog • Numbering systems • Decimal (Base 10) • Binary (Base 2) • Hexadecimal (Base 16) • Octal (Base 8) • Number conversion • Binary arithmetic • 1’s and 2’s complements of binary numbers

  3. Number & codes (2) • Signed/Unsigned numbers • Arithmetic operations with signed numbers • Coded • Binary-Coded-Decimal (BCD)/ 8421 • ASCII • Gray • Excess-3) • Error Detecting and Correction Codes • Floating Point Numbers

  4. Digital vs. Analog • 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 (0/1).

  5. Digital vs. Analog (cont.) • Digital system: • combination of devices designed to manipulate logical information or physical quantities that are represented in digital forms • Analog system: • contains devices manipulate physical quantities that are represented in analog forms

  6. Digital vs. Analog (cont.)

  7. Digital vs. Analog (cont.) • 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 : easily be recognized even among all that noise : either 0 or 1 Analog : never get back a perfect copy of the original signal

  8. Digital Techniques • Advantages: • Easier to design • Information storage is easy • Accuracy and precision are greater • Operation can be programmed - simple • Digital circuits less affected by noise • More digital circuitry can be fabricated on IC chips • Limitations: • In real world there are analog in nature and these quantities are often I/O that are being monitored, operated on, and controlled by a system. Thus, conversion and re-conversion in needed

  9. Analog Waveform

  10. Digital Waveform

  11. Introduction to Numbering Systems • We are familiar with decimal number systems for daily used such as 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

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

  13. Dec Hex Octal Binary 000000010010 0011 0100 0101 0110 0111 1000 1001 1010 1011 1100 1101 1110 1111 0123456789ABCDEF 0123456789101112131415 00010203040506071011121314151617 Numbering Systems (cont.) N U M B E R S Y S T E M S

  14. Significant Digits Binary : 1 0 1 1 0 1 Most Significant Bit Least Significant Bit (MSB) (LSB) Hexadecimal: 1 D 6 3 A 7 Most Significant Digit Least significant Digit (MSD) (LSD)

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

  16. Binary Number System (base 2) • Base 2 system: (0 , 1) • used to model the series of computer electrical signals represent the informations. • 0 represents the no voltage or an ‘off’ state • 1 represents the presence of voltage or an ‘on’ state • Example: 1012 1 0 1 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. Octal Number System (base 8) • Base 8 system: (0,1,………,7) • multiplication and division algorithms for conversion to and from base 10 • example: 7568 convert to decimal 7 5 6 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 6 1111011102

  18. Hexadecimal Number System (base 16) • Base 16 system • Uses digits 0 ~ 9 & letters A,B,C,D,E,F • Groups of four bits represent each base 16 digit

  19. Hexadecimal Number System (2) • Base 16 system • multiplication and division algorithms for conversion to and from base 10 • example : A9F16 convert to decimal A 9 F 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 : A9F16 convert to binary • A 9 F 1010100111112

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

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

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

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

  24. Hexadecimal to Decimal Conversion • Convert 3B4F16 to its decimal equivalent: Hex Digits 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 MSB LSB 1 = 0 + 1 2 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 Answer: 1 1 0 0 1.0 1 0 1

  28. Decimal to Octal Conversion Convert 42710 to its octal equivalent: 427 / 8 = 53 R3 Divided 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 6538

  29. Decimal to Hexadecimal Conversion Convert 83010 to its hexadecimal equivalent: 830 / 16 = 51 R 14 51 / 16 = 3 R3 3 / 16 = 0 R3 = E in Hex 33E16

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

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

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

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

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

  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. Substitution Code (1) Convert (010101101010111001101010)2 to hex using the 4-bit substitution code : 0101 0110 1010 1110 0110 1010 5 6 A E 6 A = 56AE6A16

  37. Substitution Code (2) Substitution code can also be used to convert binary to octal by using 3-bit groupings: 010 101 101 010 111 001 101 010 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 101 1 10102 • 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. 1’s complements of binary numbers • 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 ****** same as applying NOT gate ******

  44. 2’s complements of binary numbers • 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 + 1 00111010

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

  46. Sign numbers • 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

  47. Sign numbers • 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

  48. Digital Codes (1) • BCD (Binary Coded Decimal) / 8421 Code • Represent each of the 10 decimal digits (0~9) as a 4-bit binary code. Example: • Convert 15 to BCD. 1 5 0001 0101 • Convert 10 to binary and BCD.

  49. Digital Codes (2) • ASCII (American Standard Code for Information Interchange) Code • Used to translate from the keyboard characters to computer language • A world standard alphanumeric code for microcomputers and computers • A 7-bit code representing 27 (128) diff. characters (26 upper case, 26 lower case, 10 numbers, 33 special characters/symbol, 33 ctrl characters • 8-bit version ASCII (USACC-II 8 or ASCII-8) represent max. of 256 characters.

  50. Digital Codes (3) • 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