M05 Digital Techniques/EIS Training Manual PDF (May 2021)

Fundamentals M5 DIGITAL TECHNIQUES/EIS Rev.−ID: 1MAY2021 Author: KrA FOR TRAINING PURPOSES ON...

Fundamentals M5 DIGITAL TECHNIQUES/EIS Rev.−ID: 1MAY2021 Author: KrA FOR TRAINING PURPOSES ONLY ELTT Release: May. 19, 2021 Topics for Cabin Base ElectricianMechanic In compliance with: EASA Part-66; UAE GCAA CAR 66; CAAS SAR−66 Category B1 M05−B1−E Training Manual For training purposes and internal use only. E Copyright by Lufthansa Technical Training GmbH (LTT). LTT is the owner of all rights to training documents and training software. Any use outside the training measures, especially reproduction and/or copying of training documents and software − also extracts there of − in any format at all (photocopying, using electronic systems or with the aid of other methods) is prohibited. Passing on training material and training software to third parties for the purpose of reproduction and/or copying is prohibited without the express written consent of LTT. Copyright endorsements, trademarks or brands may not be removed. A tape or video recording of training courses or similar services is only permissible with the written consent of LTT. In other respects, legal requirements, especially under copyright and criminal law, apply. Lufthansa Technical Training Dept HAM US Lufthansa Base Hamburg Weg beim Jäger 193 22335 Hamburg Germany E-Mail: [email protected] Internet: www.LTT.aero Revision Identification: S The revision-tag given in the column ”Rev-ID” on the face S Dates and author’s ID, which may be given at the S The LTT production process ensures that the Training of this cover is binding for the complete Training Manual. base of the individual pages, are for information about Manual contains a complete set of all necessary pages in the latest revision of the content on that page(s) only. the latest finalized revision. Lufthansa Technical Training DIGITAL TECHNIQUES/EIS EASA PART-66 M05 M05 DIGITAL TECHNIQUES/EIS FOR TRAINING PURPOSES ONLY! HAM US/O53 KrA Sep 30, 2020 ATA DOC Page 1 Lufthansa Technical Training DIGITAL TECHNIQUES/EIS EASA PART-66 M5 ELECTRONIC INSTRUMENT SYSTEMS Introduction M5.1 M5.1 ELECTRONIC INSTRUMENT SYSTEMS INTRODUCTION Name Operation For the indication, all modern aircraft use electronic display devices. All modern aircraft uses digital technology in a number of ways: The names of the specific system may vary between manufacturers. S Pilot operation of a push button on a cockpit control panel will be acted on Usually, the name is Electronic Instrument System, or in short EIS. by the processor and transmitted via the data bus to the receiver systems. S Calculations in the system are made by CPUs (central processing units). Advantages S The interconnection between the electronic units is realized by digital data The advantages that make them superior to analogue meters are: buses. S Variability and Variety S Necessary parameters are fed S Coloured Displays − via display data buses to CPU−controlled CRT− or LCD− displays − via digital data busses to an on-board maintenance system (if installed). S Data is filtered: Important Data is accentuated, temporarily unimportant is suppressed. S If one monitor fails its information can be transferred to an other monitor. S Less Components needed: monitors for EIS are same type in an aircraft. FOR TRAINING PURPOSES ONLY! HAM US/O53 KrA Sep 18, 2020 01|Introduction|L1|AB12|App Page 2 Lufthansa Technical Training DIGITAL TECHNIQUES/EIS EASA PART-66 M5 ELECTRONIC INSTRUMENT SYSTEMS Introduction M5.1 Control Panel First Officer’s Panel FOR TRAINING PURPOSES ONLY! Pedestal Figure 1 Cockpit Layout HAM US/O53 KrA Sep 18, 2020 01|Introduction|L1|AB12|App Page 3 Lufthansa Technical Training DIGITAL TECHNIQUES/EIS EASA PART-66 M5 ELECTRONIC INSTRUMENT SYSTEMS Typical System Arrangements M5.1 SYSTEM ARRANGEMENT Components Displays A typical Electronic Instrument System has the following components: Displays are mainly used for two purposes: S Display Computers S Navigation S Display Units S Information about the aircraft S Control Panels. There are three generation of display units: S In the early 80’s simple cathode ray tubes were installed as displays. They Display Computers received video signals from the display computers. Display computers receive various inputs from many aircraft systems and send S In the late 80’s display units were installed. They received data and had an these data to the Displays. integrated symbol generator. Cathode ray tube and symbol generator form The inputs are: a display unit. S Navigation data (digital) S Since the 90’s LCD display units are installed in new aircraft. S Auto Flight System data (digital) Navigation S Engine data (digital) The navigation data and the information about the activities of the auto flight S Data from various aircraft systems (digital and analogue) system are displayed on the Electronic Flight Instruments. There are at least two display computers. Large aircraft have a third display Each pilot has two Display Units: computer for redundancy. S Primary Flight Display (PFD) The arrangement which computer supplies which display unit depends on the type specific engineering. S Navigation Display (ND) EFIS Technical Information EFIS is the Electronic Flight Instrument System. It is a part of the Electronic Most aircraft types have two display units which show engine data and some Instrument System EIS and shows navigation data. data from aircraft systems like the air conditioning system, the hydraulic system and some others. Some manufacturers use the name EFIS for the complete EIS system. One of these displays additionally shows alerts from various aircraft systems if FOR TRAINING PURPOSES ONLY! Control Panels something is out of limit. Since there are many data from the navigation systems each pilot can select on a related EFIS Control Panel what he wants to see on his navigation display (ND). For the centre displays there is one control panel. It is used to select the system which is appropriate to be monitored. Additionally, there are features to handle the alerts. HAM US/O53 KrA Sep 18, 2020 02|System Page 4 Arrangement|L1|AB12|App Lufthansa Technical Training DIGITAL TECHNIQUES/EIS EASA PART-66 M5 ELECTRONIC INSTRUMENT SYSTEMS Typical System Arrangements M5.1 EFIS EFIS Engine/Alert Display ND PFD ND PFD digital data analog data System Display Schematic created by Rainer Werner Copyright at Lufthansa Technical Training GmbH FOR TRAINING PURPOSES ONLY! Display Computer Display Computer Display Computer (spare) Engine Data and Aircraft System Data Various Navigation and Autoflight Systems Various Navigation and Autoflight Systems LTT Figure 2 Electronic Instrument System Arrangement HAM US/O53 KrA Sep 18, 2020 02|System Page 5 Arrangement|L1|AB12|App Lufthansa Technical Training DIGITAL TECHNIQUES/EIS EASA PART-66 M5 ELECTRONIC INSTRUMENT SYSTEMS Cockpit Layout M5.1 CLASSIFICATION OF THE INDICATORS General Aircraft Surveillance Despite the massive amount of indicators in the cockpit the indicators could be Aircraft surveillance consists of assigned to two groups: Surface Indicators like S Flight surveillance and S Position indication S Aircraft surveillance S Pressure indication and Flight Surveillance Engine surveillance like Flight surveillance is: S RPM indicators S Artificial Horizon S Exhaust Gas Temperature indicators S Heading Indicator S Fuel indicators. S Altimeter S Speed Indicator S Machmeter S Variometer S Rate of Turn Indicator S Magnetic Compass The EFIS Indicators display the most important information for flying. One may derive between: S Information on the Primary Flight Display (PFD, which in general represents the look ahead S and Information on the Navigation Display (ND), which is a look from above. FOR TRAINING PURPOSES ONLY! HAM US/O53 KrA SEP 18, 2020 03|Classification|L2|AB12|App Page 6 Lufthansa Technical Training DIGITAL TECHNIQUES/EIS EASA PART-66 M5 ELECTRONIC INSTRUMENT SYSTEMS Cockpit Layout M5.1 FOR TRAINING PURPOSES ONLY! Engine Indications Captain’s Flight Instruments First Officer’s Flight Instruments Figure 3 Cockpit Layout Boeing 747−100 HAM US/O53 KrA SEP 18, 2020 03|Classification|L2|AB12|App Page 7 Lufthansa Technical Training DIGITAL TECHNIQUES/EIS EASA PART-66 M5 ELECTRONIC INSTRUMENT SYSTEMS Cockpit Layout M5.1 FOR TRAINING PURPOSES ONLY! Captain’s EFIS First Officer’s EFIS Figure 4 Cockpit Layout Boeing 737−300 HAM US/O53 KrA SEP 18, 2020 03|Classification|L2|AB12|App Page 8 Lufthansa Technical Training DIGITAL TECHNIQUES/EIS EASA PART-66 M5 ELECTRONIC INSTRUMENT SYSTEMS Cockpit Layout M5.1 FOR TRAINING PURPOSES ONLY! Figure 5 Cockpit Layout Airbus A340 HAM US/O53 KrA SEP 18, 2020 03|Classification|L2|AB12|App Page 9 Lufthansa Technical Training DIGITAL TECHNIQUES/EIS EASA PART-66 M5 ELECTRONIC INSTRUMENT SYSTEMS Cockpit Layout M5.1 CONTROL Name The indication system for the aircraft surveillance may have different names. Boeing names it EICAS. This means Engine Indicating and Crew Alerting System. Airbus names it ECAM. This means Electronic Centralized Aircraft Monitor. EICAS or ECAM are part of the EIS. Display Controls The position of the brightness control knob usually is besides the displays in a vertical position. Brightness can be set by rotary knobs. In addition brightness is controlled automatically by light sensors attached to the displays. The brightness control for the Navigational Display consists of two knobs. A separate control is available for the basic indication on the ND and for the weather radar indication, which is an overlay to the navigation information. In bright sunlight it may be more difficult to read the indication on glass cockpit screens than on analogue indicators because of the limitation in brightness of the screens. OFF Position On Airbus aircraft the control knobs have a dedicated OFF position, displays are switched off if set to the extreme left. On Boeing aircraft an OFF position is not available. If brightness control is set to minimum the displays are still active as long as power supply is available. FOR TRAINING PURPOSES ONLY! HAM US/O53 KrA Sep 18, 2020 05|Control|L1|AB12|App Page 10 Lufthansa Technical Training DIGITAL TECHNIQUES/EIS EASA PART-66 M5 ELECTRONIC INSTRUMENT SYSTEMS Cockpit Layout M5.1 FOR TRAINING PURPOSES ONLY! Figure 6 EIS Brightness Control HAM US/O53 KrA Sep 18, 2020 05|Control|L1|AB12|App Page 11 Lufthansa Technical Training DIGITAL TECHNIQUES/EIS EASA PART-66 M5 ELECTRONIC INSTRUMENT SYSTEMS Typical System Arrangements M5.1 INDICATION IN CASE OF A COMPUTER FAILURE General If a computer fails the indication changes. On Airbus aircraft a white line is displayed. On Boeing aircraft the screen turns dark. FOR TRAINING PURPOSES ONLY! HAM US/O53 KrA Sep 18. 2020 06|Failure|L2|B12|App Page 12 Lufthansa Technical Training DIGITAL TECHNIQUES/EIS EASA PART-66 M5 ELECTRONIC INSTRUMENT SYSTEMS Typical System Arrangements M5.1 FOR TRAINING PURPOSES ONLY! Figure 7 Display in case of a Computer Failure HAM US/O53 KrA Sep 18. 2020 06|Failure|L2|B12|App Page 13 Lufthansa Technical Training DIGITAL TECHNIQUES/EIS EASA PART-66 M5 NUMBERING SYSTEMS Numbering Systems M5.2 M5.2 NUMBERING SYSTEMS INTRODUCTION General Identification of the System A knowledge of numbering systems is essential for understanding computers For the usual numbering systems there is a letter code. and their operation. Digital Techniques have components which calculate by numbers. The Numbering System Base Designation numbering system they use is not the numbering system which is commonly Binary 2 B used by us in everyday life. All numbering systems are used to count objects or perform mathematical Octal 8 Q (instead of O) calculations and each consists of a set of symbols and characters, commonly Decimal 10 D referred to as digits. Hexadecimal 16 H Base Every numbering system has a base which describes the system and is equal to the number of values a digit can have. A subscript is often added to a number to indicate its base. An example of this is 1012, which indicates the number 101 is a base 2 or binary number. The value of the largest digit of a numbering system is one less than the base and the value of the smallest digit of a numbering system is zero. Each digit is multiplied by the base raised to the appropriate power for the digit position. Positional Notation The standard shorthand form of writing numbers is known as positional notation. The value of a particular digit depends not only on the digit value, but also on the position of the digit within the number. FOR TRAINING PURPOSES ONLY! The digit at the far right is called the Least Significant Digit (LSD) and the digit at the far left is called the Most Significant Digit (MSD). HAM US/O53 KrA Sep 18, 2020 01|Introduction|L1|B12|Eng|App Page 14 Lufthansa Technical Training DIGITAL TECHNIQUES/EIS EASA PART-66 M5 NUMBERING SYSTEMS Numbering Systems M5.2 THIS PAGE INTENTIONALLY LEFT BLANK FOR TRAINING PURPOSES ONLY! HAM US/O53 KrA Sep 18, 2020 01|Introduction|L1|B12|Eng|App Page 15 Lufthansa Technical Training DIGITAL TECHNIQUES/EIS EASA PART-66 M5 NUMBERING SYSTEMS Decimal System M5.2 DECIMAL NUMBER SYSTEM General The decimal number system (base 10) is the most familiar, and is used for everyday counting and mathematical calculations. This numbering system contains ten digits from 0 to 9. Example 1 For example, the decimal number 4738 is standard shorthand form for the quantity four thousand seven hundred thirty-eight. If the base 10 shall be indicated, the writing is 473810. Each position has a ”value” or “weight”. Starting at the right is the units position, next the tens, then hundreds, and at the left is the thousands position. The decimal number 4738 is equal to (4 10 3))(7 102))(3 101))(8 100) 4738 = 4 x 103 + 7 x 102 + 3 x 101 + 8 x 100 Example 2 105 104 103 102 101 100 10−1 10−2 Weighted Value 6 5 8 9 1 2 3 3 Number 600.000 50.000 8.000 900 10 2 0.3 0.03 FOR TRAINING PURPOSES ONLY! The total result is 600.000 + 50.000 + 8.000 + 900 + 10 + 2 + 0.3 + 0.03 = 658912.33 HAM US/O53 KrA Sep 18, 2020 02|Decimal System|L1|B12|Eng|App Page 16 Lufthansa Technical Training DIGITAL TECHNIQUES/EIS EASA PART-66 M5 NUMBERING SYSTEMS Decimal System M5.2 THIS PAGE INTENTIONALLY LEFT BLANK FOR TRAINING PURPOSES ONLY! HAM US/O53 KrA Sep 18, 2020 02|Decimal System|L1|B12|Eng|App Page 17 Lufthansa Technical Training DIGITAL TECHNIQUES/EIS EASA PART-66 M5 NUMBERING SYSTEMS Binary System M5.2 BINARY NUMBER SYSTEM Introduction General The simplest number system employing positional notation is the binary system. As the name implies, the system has a base of 2. The two binary digits used are 0 and 1. In a digital computer, only two distinct states exist. Therefore, all inputs to a digital computer must be converted to a series of 1’s and 0’s (binary) before the computer can make use of the data. These 1’s and 0’s can be used to describe the status of a system, e.g.: Voltage applied: =1 No voltage applied: =0 Digit... 5th 4rd 3rd 2nd 1st Weighted Value 24 23 22 21 20 Base 10 Value 16 8 4 2 1 Bit A digit is also called a bit. FOR TRAINING PURPOSES ONLY! HAM US/O53 KrA Sep 18, 2020 03|Binary System|L1|B12|Eng|App Page 18 Lufthansa Technical Training DIGITAL TECHNIQUES/EIS EASA PART-66 M5 NUMBERING SYSTEMS Binary System M5.2 Conversions Binary to Decimal Conversions Decimal to Binary Conversions Conversion from binary to decimal is straightforward and easily performed using A mathematical method of conversion is to repeatedly divide the decimal positional notation. number by the base number, and by keeping track of the remainders, the new In the example, the weighted value of each bit position (20 , 21 ,22...) and the numbering base equivalent is obtained. base 10 equivalent for each bit position is shown. In the case of decimal to binary conversions, the decimal number is To convert 1011 (base 2) to base 10 add together the base 10 value for each successively divided by the base number 2. The first remainder obtained is the bit position containing a 1. least significant digit (LSD), and the last remainder is the most significant digit (MSD). The bit at the far right is the Least Significant Digit (LSD) and the bit at the far left is the Most Significant Digit (MSD). Values of Digits: 8421 Decimal Number: 105D Given: 10112 Equivalent Binary Number 1101001B LSB Decimal number 8 + 0 + 2 + 1 = 1110 1 0 5 : 2 = 52 Rem. 1 5 2 : 2 = 26 Rem. 0 The digit for the value four is disregarded 2 6 : 2 = 13 Rem. 0 because there are zero of these values to be 13 : 2 = 6 Rem. 1 added. 6 : 2 = 3 Rem. 0 3 : 2 = 1 Rem. 1 1 : 2 = 0 Rem. 1 MSB MSB means Most Significant Bit FOR TRAINING PURPOSES ONLY! LSB means Least Significant Bit This principle can be used for each and every numbering system. It can easily be used for computer programs. HAM US/O53 KrA Sep 18, 2020 03|Binary System|L1|B12|Eng|App Page 19 Lufthansa Technical Training DIGITAL TECHNIQUES/EIS EASA PART-66 M5 NUMBERING SYSTEMS Binary System M5.2 Examples Example 1 Convert 1001 to a Decimal Write down the powers of 2 and add them to a sum. 1 x 23 = 8 + 0 x 22 = 0 + 0 x 21 = 0 + 1 x 20 = 1 9 Thus 1001 2 is equal to 9 10 Example 2 Convert 1001001 to a Decimal Write down the powers of 2, and the number to be converted below them, as follows: 64 32 16 8 4 2 1 1 0 0 1 0 0 1 Then add all the numbers above the 1’s i.e. 64 + 8 + 1 = 73 Example 3 Convert 271 to Binary Every figure in the decimal numeral system can be broken down into powers of 2 and thus can be transferred to the binary numeral system. FOR TRAINING PURPOSES ONLY! HAM US/O53 KrA Sep 18, 2020 03|Binary System|L1|B12|Eng|App Page 20 Lufthansa Technical Training DIGITAL TECHNIQUES/EIS EASA PART-66 M5 NUMBERING SYSTEMS Binary System M5.2 Method 1 Find the powers of two which is equal or smaller than the number to be converted. For 271 this is 2 8, that equals 256 10. 256 128 64 32 16 8 4 2 1 2 = 256 fits one time in the 271. 8 Write a 1 under the 256. Subtract 256 from 271. 271 − 256 = 15 2 7 doesn’t fit into the remaining in the 15, so note a 0. The same is with 2 6, 2 5 and 2 4. Here you also note a 0 for each. Then 2 3 = 8 fits one time in the 15, so you note a 1, please. Subtract 8 from 15. 15 - 8 = 7 2 2 = 4 fits one time in the 7, so you note a 1. Subtract 4 from 7. 7-4=3 2 1 = 2 fits one time in the 3, so you note a 1. Subtract 2 from 3. 3-2=1 2 0 = 1 fits one time in the 1, so you note a 1. The result of all the 1 and 0 is: 100001111 Method 2 FOR TRAINING PURPOSES ONLY! If you write all the powers of 2 in a line and then the zeros and ones below, you get the following result: First write all powers of two, beginning with the highest number which has to be used for the calculation. Again, 256 in this case. 256 128 64 32 16 8 4 2 1 1 0 0 0 0 1 1 1 1 The decimal number 271 10 therefore is 100001111 2 HAM US/O53 KrA Sep 18, 2020 03|Binary System|L1|B12|Eng|App Page 21 Lufthansa Technical Training DIGITAL TECHNIQUES/EIS EASA PART-66 M5 NUMBERING SYSTEMS Octal System M5.2 OCTAL NUMBER SYSTEM Introduction converted to octal is repeatedly divided by the base 8 and again the remainders are used for the decimal to octal equivalent number. General Successive division by Base Number: Numerical operations in microcomputers are performed by binary numbers, Example when used to represent large quantities many 0’s and 1‘s are needed. This is Convert 238610 to octal by using successive division. cumbersome and time−consuming; therefore, other systems are often used as a shorthand notation for binary numbers. 2386 / 8 = 298R 2 One popular system is the octal system which was very common until the mid 298 / 8 = 37 R 2 70ties. 37 /8 = 4 R5 The octal system base is 8. 4 /8 = 0 R4 The digits 0 through 7 are available, 8 and 9 do not exist. 238610 = 45228 As a result, frequent binary−to−octal conversions are necessary. Binary to Octal Conversion Powers of 8 In binary, three−bit positions represent exactly eight combinations (000 through 111). Therefore, octal numbers can be directly substituted for 3−bit binary Powers of 8; 84 83 82 81 80 numbers. The binary number is separated into groups of three bits beginning at Decimal No: 4096 512 64 8 1 the right with the least significant digit (LSD) and proceeding to the most It is possible to show values which are smaller than 1: significant digit (MSD) at the left. Each group of three bits is then replaced by 8 *1 equals 0.125 in the decimal system. an octal equivalent. In forming the 3−bit groupings, 0’s may need to be added to complete the most 8 *2 equals 0.015625 in the decimal system. significant digit (MSD). In the positional notation example, the weighted value of each bit position (80, 81, 82...) and the base 10 equivalent are shown. Octal−to−binary conversion is the reverse of the above procedure. This is easily accomplished by replacing each octal digit by its 3−bit binary equivalent. To convert 4522 (base 8) to base 10, multiply each octal digit by its corresponding base 10 value, then add together the computed base 10 values. FOR TRAINING PURPOSES ONLY! Digit... 5th 4rd 3rd 2nd 1st Weighted Value 84 83 82 81 80 Base 10 Value 4096 512 64 8 1 Conversions Octal to Decimal Conversion As in the case of decimal to binary conversions, decimal to octal conversions can also be accomplished by successive division. The decimal number to be HAM US/O53 KrA Sep 18, 2020 06|Octal System|L2|B12|Eng|App Page 22 Lufthansa Technical Training DIGITAL TECHNIQUES/EIS EASA PART-66 M5 NUMBERING SYSTEMS Octal System M5.2 Converting Binary to Octal Converting Octal to Binary To convert a binary number to an octal number, construct a 3−bit binary / octal For the conversion of octal numbers to binary numbers, just use the table in a look-up table like the one below. Starting at the binary decimal point of the reverse manner. binary number, take the first 3 bits and find the corresponding octal value from To convert from octal to binary, write down the binary representation of each the table. octal digit. Note that each octal digit should take up 3 bits. 3−bit binary / octal table Example: Convert 322 8to binary 3−bit Binary Octal 3 = 011 000 0 2 = 010 001 1 2 = 010 010 2 so, 322 8 = 011010010 2 011 3 100 4 101 5 110 6 111 7 3−bit Binary/Octal table Start with the 3 most right bits and find the related octal value in the table. Repeat this with the next 3 bits and so on. If there are less than 3 bits left, fill with zeroes until you have 3 bits. Again, use the table. Example Convert 11010010 to octal. 1. Take the 3 most right bits, 010 and find the corresponding octal value in the FOR TRAINING PURPOSES ONLY! above look−up table. The octal value is 2. 2. Take the next 3 bits, 010. The corresponding octal value from the look−up table is 2 again. 3. Now only 2 bits, 11 of the binary number remain. Pad the left hand side with a 0 to get 011. The corresponding octal from the look−up table is 3. so, 11010010 2 + 3228 HAM US/O53 KrA Sep 18, 2020 06|Octal System|L2|B12|Eng|App Page 23 Lufthansa Technical Training DIGITAL TECHNIQUES/EIS EASA PART-66 M5 NUMBERING SYSTEMS Octal System M5.2 THIS PAGE INTENTIONALLY LEFT BLANK FOR TRAINING PURPOSES ONLY! HAM US/O53 KrA Sep 18, 2020 06|Octal System|L2|B12|Eng|App Page 24 Lufthansa Technical Training DIGITAL TECHNIQUES/EIS EASA PART-66 M5 NUMBERING SYSTEMS Octal System M5.2 BINARY TO OCTAL OCTAL TO BINARY 0111000012 2258 011 100 0012 2 2 58 3 4 18 010 010 1012 FOR TRAINING PURPOSES ONLY! 3418 0100101012 Figure 8 Binary to Octal / Octal to Binary HAM US/O53 KrA Sep 18, 2020 06|Octal System|L2|B12|Eng|App Page 25 Lufthansa Technical Training DIGITAL TECHNIQUES/EIS EASA PART-66 M5 NUMBERING SYSTEMS Hexadecimal System M5.2 HEXADECIMAL NUMBER SYSTEM Introduction General Hexadecimal Number Decimal Equivalent The hexadecimal number system is another system often used in 0 0 micro-computers. It has a base of 16 which requires sixteen digits. The digits used are 0 through 9 and A through F. The symbols A through F represent the 1 1 equivalent decimal numbers of 10 through 15, respectively. 2 2 This system is called an alphanumeric number system since numbers and 3 3 letters are used to represent its digits. In the positional notation example, the weighted value of each digit’s position 4 4 (160,161,162...) and the base 10 equivalent is shown. 5 5 6 6 A → 10 B → 11 7 7 C → 12 8 8 D → 13 9 9 E → 14 A 10 F → 15 B 11 C 12 Often hexadecimal numbers are written with an “H” following the number to denote they are hexadecimal numbers. D 13 E 14 F 15 FOR TRAINING PURPOSES ONLY! HAM US/O53 KrA Sep 18, 2020 07|HEX System|L2|B12|Eng|App Page 26 Lufthansa Technical Training DIGITAL TECHNIQUES/EIS EASA PART-66 M5 NUMBERING SYSTEMS Hexadecimal System M5.2 Conversions Decimal / Hexadecimal Conversion Decimal to hexadecimal conversions may be done by successive division In this case, the decimal number is divided by the base number of 16. If the remainder is greater than 9, it should be changed to the hexadecimal equivalent of the remainder. For example, if the remainder is 10, It should be changed to ”A”; if the remainder is 11, it should be changed to ”B”, and so on, up to 15, which is ”F”. Example Convert 4325810 to hexadecimal by using successive division. 43253/ 16 = 2703 R5 2703 / 16 = 168 R F (15) 168 / 16 = 10 R8 10 / 16 = 0 R A (10) 4325310 = A8F516 Digit... 5th 4rd 3rd 2nd 1st Weighted Value 164 163 162 161 160 Base 10 Value 65536 4096 256 16 1 Number to be converted A 8 F 5 Equivalent Base 10 Number 40960 2048 240 5 To convert A8F5 (base 16) to base 10, multiply each hexadecimal digit by its FOR TRAINING PURPOSES ONLY! corresponding base 10 value then add together the computed base 10 values. 40960 + 2048 + 240 + 5 = 4325310 A8F516 = 4325310 Figure 9 Hexadecimal Number System HAM US/O53 KrA Sep 18, 2020 07|HEX System|L2|B12|Eng|App Page 27 Lufthansa Technical Training DIGITAL TECHNIQUES/EIS EASA PART-66 M5 NUMBERING SYSTEMS Hexadecimal System M5.2 Binary / Hexadecimal Conversion The hexadecimal number system is used as a shorthand notation for binary numbers. In binary, 4− bit positions are necessary to obtain sixteen combinations (0000 to 1111). As a result of this, hexadecimal numbers can be directly substituted for 4−bit binary numbers. The binary number is separated into groups of four bits beginning at the LSD and preceding to the left. Each group of four bits is then replaced by hexadecimal equivalent. In forming the 4−bit groupings, 0’s may be required to complete the first (MSD) group. Hexadecimal−to−binary conversion is the inverse of the above procedure. This is easily performed by replacing each hexadecimal digit by its 4−bit binary equivalent. FOR TRAINING PURPOSES ONLY! HAM US/O53 KrA Sep 18, 2020 07|HEX System|L2|B12|Eng|App Page 28 Lufthansa Technical Training DIGITAL TECHNIQUES/EIS EASA PART-66 M5 NUMBERING SYSTEMS Hexadecimal System M5.2 BINARY TO HEXADECIMAL HEXADECIMAL TO BINARY 10101000111101012 F13A16 1010 1000 1111 01012 F 1 3 A16 A 8 F 516 1111 0001 0011 10102 FOR TRAINING PURPOSES ONLY! A8F516 11110001001110102 Figure 10 Binary and Hexadecimal Conversions HAM US/O53 KrA Sep 18, 2020 07|HEX System|L2|B12|Eng|App Page 29 Lufthansa Technical Training DIGITAL TECHNIQUES/EIS EASA PART-66 M5 NUMBERING SYSTEMS Numbering Systems M5.2 OVERVIEW Binary-, Octal-, Hexadecimal Numbering System In case we count in the binary system a specific arrangement will be the result. This arrangement shows the relation between the numbers from the different numbering systems. As the octal system is a grouping of 3 bit, the hexadecimal system is a grouping of 4 bit octal-hexadecimal conversions are very simple: Example The octal 123 is to be converted into hexadecimal. 1238 as a binary is 001 010 0112 As a hexadecimal is a re-grouping into groups of 4: 0 0101 00112 as a hex is 05316. FOR TRAINING PURPOSES ONLY! HAM US/O53 KrA Sep 18, 2020 09|Overview|L1|B12|Eng|App Page 30 Lufthansa Technical Training DIGITAL TECHNIQUES/EIS EASA PART-66 M5 NUMBERING SYSTEMS Numbering Systems M5.2 OVERVIEW DECIMAL, BINARY, OCTAL AND HEXADECIMAL NUMBERING SYSTEM Decimal Binary Octal Hexadecimal 101 100 24 23 22 21 20 81 80 161 160 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 0 1 0 2 0 0 0 1 0 0 2 0 2 0 3 0 0 0 1 1 0 3 0 3 0 4 0 0 1 0 0 0 4 0 4 0 5 0 0 1 0 1 0 5 0 5 0 6 0 0 1 1 0 0 6 0 6 0 7 0 0 1 1 1 0 7 0 7 0 8 0 1 0 0 0 1 0 0 8 0 9 0 1 0 0 1 1 1 0 9 1 0 0 1 0 1 0 1 2 0 A 1 1 0 1 0 1 1 1 3 0 B 1 2 0 1 1 0 0 1 4 0 C 1 3 0 1 1 0 1 1 5 0 D 1 4 0 1 1 1 0 1 6 0 E 1 5 0 1 1 1 1 1 7 0 F 1 6 1 0 0 0 0 2 0 1 0 FOR TRAINING PURPOSES ONLY! 1 7 1 0 0 0 1 2 1 1 1 1 8 1 0 0 1 0 2 2 1 2 1 9 1 0 0 1 1 2 3 1 3 2 0 1 0 1 0 0 2 4 1 4 2 1 1 0 1 0 1 2 5 1 5 2 2 1 0 1 1 0 2 6 1 6 2 3 1 0 1 1 1 2 7 1 7 HAM US/O53 KrA Sep 18, 2020 09|Overview|L1|B12|Eng|App Page 31 Lufthansa Technical Training DIGITAL TECHNIQUES/EIS EASA PART-66 M5 LOGIC CIRCUITS Logic Circuits M5.5 M5.5 LOGIC CIRCUITS Introduction General Positive and Negative Logic Digital Computers and Central Processor Units must be able to realize The assignment depends on the technology used, you can say „it is at will“. arithmetic processes and logical combinations, which are both made in a so This assignment gives us the so called positive Logic and negative Logic. called ALU (Arithmetic Logic Unit), the heart of each CPU ( Central Processor Unit ). Positive Logic Negative Logic This ALU needs the inputs in digital form: 1»H 1»L S logic 1 (also known as logic ’’True’’), 0»L 0»H S logic 0 (also known as logic ’’False‘‘). Usually the H-Level is seen as „1“, L-Level is to be seen as „0“. Bit H means 1 L means 0 The single item of information (logic 1 or logic 0) is known as a ’’bit’’ (binary digit). H means high voltage, L means low voltage. However, the voltages used in Level Assignment digital techniques are relatively low since no power needs to be applied on mechanical devices. A binary signal is a digital signal with only two different values. A special meaning is assigned to these two values (voltages): Operators Example Operators are signs in mathematics. In logic circuits, they show how the input Voltage applied ³ U = 1. signals are combined to calculate the output signal. No voltage applied ³ U = 0. For logic’s, the following operators are used: A fulfilled condition is considered to be logic „1“, otherwise it is logical „0“. This S AND ƞ is just a logic state, not a value or Voltage. S OR Ɵ An assignment has to be made in accordance with the hardware requirements. S NOT þ FOR TRAINING PURPOSES ONLY! Usually we say: the voltage level that is more positive is seen as „“1“, the voltage level that more negative is to be seen logic „0“. Mixed Logic Individual assignments may be used. We call them mixed logic. This system has the disadvantage that some inverted gates are not available. HAM US/O53 KrA Sep 18, 2020 01|Introduction|L2|B12|Eng|App Page 32 Lufthansa Technical Training DIGITAL TECHNIQUES/EIS EASA PART-66 M5 LOGIC CIRCUITS Logic Circuits M5.5 +U System A System B System C H H L H L L FOR TRAINING PURPOSES ONLY! −U Figure 11 Level Assignment HAM US/O53 KrA Sep 18, 2020 01|Introduction|L2|B12|Eng|App Page 33 Lufthansa Technical Training DIGITAL TECHNIQUES/EIS EASA PART-66 M5 LOGIC CIRCUITS Identification of common logic gate symbols, tables M5.5 Basic Functions General The illustration with the logic symbols is completely independent from the technology used. It just states the function but not the „contents“. For logical combination there are only three basic functions: S AND Function S OR Function S INVERTER Function. AND Gate An AND-Gate may have two or more inputs ( E1 to En ) and one output ( A ). The output has only a logical 1, if all inputs have a logic 1. If one or more inputs have a logic 0, the output has a logic 0. Switching Function A = E1 x E2 x..... x En or A = E1 Λ E2 Λ.....Λ En A equals E1 and E2 and..... and En Truth Table (for two Inputs) E2 E1 A 0 0 0 0 1 0 1 0 0 FOR TRAINING PURPOSES ONLY! 1 1 1 HAM US/O53 KrA Sep 18, 2020 04|Basic Functions|L2|B12|Eng|App Page 34 Lufthansa Technical Training DIGITAL TECHNIQUES/EIS EASA PART-66 M5 LOGIC CIRCUITS Identification of common logic gate symbols, tables M5.5 E1 E1 & A A E2 E2 En En DIN / IEC / ANSI MIL / ANSI AND Symbols E1 E2 U ÉÉ ÉÉ E1 ÉÉ ÉÉ Contact Plan ÉÉÉÉ E2 ÉÉ ÉÉÉÉ ÉÉ ÉÉÉÉ FOR TRAINING PURPOSES ONLY! A ÉÉ ÉÉ ÉÉ ÉÉ Impulse Diagram Figure 12 AND Gate HAM US/O53 KrA Sep 18, 2020 04|Basic Functions|L2|B12|Eng|App Page 35 Lufthansa Technical Training DIGITAL TECHNIQUES/EIS EASA PART-66 M5 LOGIC CIRCUITS Identification of common logic gate symbols, tables M5.5 OR Gate An OR-Gate may have two or more inputs ( E1 to En ) and one output ( A ). The output has only a logical 1, if one or more inputs have a logic 1. The out put has only a logic 0, if all inputs have a logic 0. Switching Function A = E1 + E2 +... + En or A = E1 v E2 v... v En A equals E1 or E2 or...... or En Truth Table (for two Inputs) E2 E1 A 0 0 0 0 1 1 1 0 1 1 1 1 FOR TRAINING PURPOSES ONLY! HAM US/O53 KrA Sep 18, 2020 04|Basic Functions|L2|B12|Eng|App Page 36 Lufthansa Technical Training DIGITAL TECHNIQUES/EIS EASA PART-66 M5 LOGIC CIRCUITS Identification of common logic gate symbols, tables M5.5 E1 y1 E1 A A E2 E2 En En DIN / IEC / ANSI MIL / ANSI OR Symbols E1 U E1 ÉÉÉ É ÉÉÉ É E2 É ÉÉÉÉ Contact Plan E2 É ÉÉÉÉ FOR TRAINING PURPOSES ONLY! A ÉÉÉ ÉÉÉ ÉÉÉÉ ÉÉÉÉ Impulse Diagram Figure 13 OR Gate HAM US/O53 KrA Sep 18, 2020 04|Basic Functions|L2|B12|Eng|App Page 37 Lufthansa Technical Training DIGITAL TECHNIQUES/EIS EASA PART-66 M5 LOGIC CIRCUITS Identification of common logic gate symbols, tables M5.5 Inverter The Inverter (NOT-Function) inverts the input signal. It is also called a Boolean complement. If the input signal is a logical 1, the output signal is a logical 0 and vice versa. Switching Function: A=E A is inverse to E Truth Table E A 0 1 1 0 FOR TRAINING PURPOSES ONLY! HAM US/O53 KrA Sep 18, 2020 04|Basic Functions|L2|B12|Eng|App Page 38 Lufthansa Technical Training DIGITAL TECHNIQUES/EIS EASA PART-66 M5 LOGIC CIRCUITS Identification of common logic gate symbols, tables M5.5 E 1 A E 1 A A E DIN / IEC / ANSI MIL / ANSI Inverter Symbols A ÉÉÉ É ÉÉÉ E1 ÉÉÉ ÉÉ U Contact Plan ÉÉ A ÉÉÉÉ ÉÉÉÉ ÉÉ ÉÉÉÉÉÉÉÉ FOR TRAINING PURPOSES ONLY! Impulse Diagram Figure 14 Inverter HAM US/O53 KrA Sep 18, 2020 04|Basic Functions|L2|B12|Eng|App