Decimal to Binary Conversion

• Computers are employed for repeated calculations and processing large data amounts, with applications in aviation, military, and scientific sectors.
• Digital computers offer advantages like speed, accuracy, and manpower savings, taking over routine tasks.
• Humans use decimal numbers, while computers use coded electronic pulses.

Numbering Systems

• Numbering systems have common components: unit, number, and base.
• Decimal: Base 10, uses 0-9
• Binary: Base 2, uses 0 and 1
• Octal: Base 8, uses 0 to 7
• Hexadecimal: Base 16, uses 0-9 and A to F

Units and Numbers

• A unit is a single object, like an apple or a dollar.
• A number is a symbol representing a unit or quantity
• Arabic numerals (0-9) are primarily used, may use letters.

Numbering Systems - Base

• The base indicates the number of symbols
• Indicated via a subscript decimal number (1010₂) following the value.
• The highest value symbol used is always one less than the base.

Positional Notation and Zero

• Positional notation: a number's value depends on its symbol and position.
• Zero: Placement affects represented value's magnitude.

Digital Numbering Systems

• Base 10 system aka Decimal is the universal method for counting. Example 12 as 12₁₀
• Base 2 system or Binary: is used by computers to perform all calculations. Example 1100 as 1100₂
• Base 8 or Octal is used in computer applications and digital systems. Example 144 as 144₈
• Base 16 system aka Hexadecimal which eases conversion from binary. Example 90 as 90₁₆

Key Binary Terms

• Bit: one binary digit
• Nibble: 4 bits; four possible values
• Byte: 8 bits
• Word: 16 bits
• Long word: 32 bits
• Very long word: 64 bits

Binary Numbering System

• The base 2 system relies on 0 and 1 symbols.
• Each position represents a power of 2.

Octal Numbering System

• Each octal numeral is represented by three binary digits for easy conversion.
• Octal numerals: 0, 1, 2, 3, 4, 5, 6, 7.

Hexadecimal Numbering System

• Base 16 uses 16 symbols: 0-9 and A-F. Each hex digit represents four binary digits
• Hex uses the decimal system's first 10 numbers, uses A for 10, B for 11, C for 12, D for 13, E for 14, F for 15

Converting Between Numbering Systems

• Binary to Decimal Conversion using the binary truth table.

Decimal to Binary Conversion - Division (Method 1)

• Repeatedly divides a decimal number by 2 and records the quotient and remainder.

Decimal to Binary Conversion - Subtraction (Method 2)

• Repeatedly subtracts powers of 2 from the decimal number.

Octal to Decimal Conversions

• The Octal number may need conversion to binary for humans to understand its decimal expression.

Decimal to Octal Conversion (Method 1)

• Convert the decimal number to binary, substitute three binary sets for the first octal digit.

Decimal to Octal Conversion (Method 2)

• To convert decimal to octal, divide the decimal number by 8. All the remainders represent the converted octal number.

Hexadecimal to Decimal Conversions

• To convert a hexadecimal number to decimal, convert the hex number to binary. Then convert the binary to decimal. As already explained by using binary truth table. One can convert directly with the hexadecimal truth table.

Decimal to Hexadecimal Conversions

• To convert Decimal numbers, it is quite difficult to use division, instead one should first convert Decimal to Binary and then Binary to Hex using the above techniques.

Data Conversion

• Data Conversion involves Analog and Digital Data

Data Conversion (5.3)

• Analog data is continuous, capturing every nuance.
• Digital data samples and encodes.
• Analog is unfiltered raw data.
• Digital is filtered data used in ADC and DAC.

Converting Between Analogue and Digital

• Analogue-to-Digital Converters (ADC) convert analogue to digital.
• Digital-to-Analogue Converters (DAC) convert digital to analogue.
• The function of an Op-amp should be understood first

Typical Data System elements for conversion between digital Analog

• Transducer

• ADC

• Computer

• DAC

• Actuator

• The physical variable gets read by transducer, this outputs the data Electrical analogue. ADC then converts to digital to be processed by a computor, a proportional analogue voltage or current is presented.

Operational Amplifiers (Op-Amps)

• Operational amplifiers compare amplitude of voltage with another
• Open-loop configuration with input voltage on one input and reference voltage on the other

Op Amp Characteristics

• High gain, order of a million.
• High-input impedance, low-output impedance.
• Split supply, usually +/- 15 V.
• Used with feedback; gain determined by feedback network

Operation of Op-Amps as Comparators

• Zero Level Detection is used to determine when an input voltage exceeds a level by grounding inverting input
• High open-loop voltage of -amps drives it to saturation upon a small difference between inputs

Non-Zero Level Detection

• Modified to detect voltages other than zero by connecting a fixed reference to inverting input
• Practical arrangement uses voltage divider to set reference voltage

Non-Inverting Amplifier

• Op-amp is connected in a closed-loop as a non-inverting amplifier.
• It has a controlled amount of voltage gain.

Inverting Amplifier

• Input signal applied to inverting input.
• Output applied back to inverting input.
• Feedback circuit forms voltage divider to reduce output voltage.

Digital to Analogue Conversion

• Digital-to-Analogue Converters: convert signals between analogue and digital
• Conversions based on a DAC or D/A converter circuit
• 1, 2, 4, and 8 digital input values are input to op-amp via weighted resistors

Binary Weighted Resistor DAC

• Converts a 4-bit binary number to a matching output voltage.
• Circuit uses +5 V as logic 1 and 0 V as logic 0.
• Digits 1, 2, 4, and 8 indicate relative weight.

R/2R Ladder DAC

• This ladder uses just two resistance values
• Temperature variations have less effect

R/2R Ladder DAC Operation

• The fundamental principle shows two parallel resistors of equal value have a circuit resistance of one half of an individual resistor

Analogue to Digital Conversion

• Analogue to digital conversion is a common interfacing process often used when a linear system must provida inputs to a digital system

Analogue to Digital Conversion Methods

• Analogue to Digital Conversion typically includes:
• Flash or simultaneous
• Digital-ramp or counter type

Flash ADC

• Determines which analogue voltage is closest to 0, 1, 2 or 3 volts, and stored as a 2-bit number
• Requires a set of comparators
• Encoder: Additional circuitry encodes signals into digital numbers.
• Requires many comparators

Flash ADC Encoder

• Flash ADC Encoder: allows the use of a simpler, non-priority encoder

Digital-Ramp ADC

• Uses a DAC and single comparator
• Uses a binary counter as a register

Data Buses (5.4)

• Data Buses use binary
• Transfer data through Digital Data Transfer

Serial Data Transfer

• Bits in sequence
• Less hardware than parallel

Parallel Data Transfer

• Each bit from separate circuit, transferred over separate line

Multiplexing

• Multiplexing. is the combining two or more channels onto a common transmission medium.
• In aircraft multiplexing decreases number of wires carrying signals.
• Digital 'time division' technique

Aircraft Multiplex System

• With digital technology, digital computers offered increased computational capabilities than anlogue systems

Data Bus systems

• Interface between computer to external device.
• Usually shielded and jacketed.
• Provide spike protection, EMF elimination, accurate transmissions.

Data Bus connectors

• Multiplexer bus acts as an arterial highway.
• Bus Controller manages data, peripheral components connect through breakouts.

Bus Controller

• Terminals are capable as BC, only one BC Active at a time
• Commands : Data transfer, Control, Management and the bus

MIL-STD-1553 Data Bus

• MIL-STD-1553 - Military Standard defines electrical and protocol characteristics for data bus

MIL-STD-1553 Data Words

• Each word length is 20 bits long.
• The 3 bits sync field Device clocks to re-sync.
• The next 16 bits are the information field
• parity bit

Data Bus information

• Data: Contains purely data, are always commanded with status.
• Status words: Contain terminal address where status word is sent.
• Bit encoding: based on Bi-Phase Manchester II format

ARINC 429

• ARINC provides Standard specifications and standards for avionics equipment
• Aircraft can equip with a different number of systems due to interconnections. ARINC details specifications for these numbers.

ARINC 429 Usage

• ARINC 429 is found in air craft's like airbus 310 - A340 as well as boeing and mcdonnel douglas

ARINC 429 Characteristics

• Used for data busses with two signal wires.
• a word size of 32 bit
• simplex data bus
• Bit encoding has bipolar return

ARINC 629

• new technology known as digital autonomous terminal access communication was being developed by boeing
• it has the design for global data bus which will have all information to get to components
• the device was to provide both coding components so this wouldn't be jumbled during exchange

Logic Circuits (5.5)

• Boolean Logic
• Representing Binary Quantities
• Digital Signals and Timing Diagrams
• Boolean Constants and Variables
• Truth Tables
• Simple Logic Gates
• Logic Gates

Boolean Logic

• Is a circuit's outputs and inputs.

Representing Binary Quantities

• Digital systems: binary used for computations.
• Two operating states/conditions.
• Open/ closed switch
• Lightbulb

Logic States

• Binary 0 is 0V.
• Binary 1 is +5V.
• Practical systems use Voltage Range.
• 0 or 0.8V == Binary zero.
• 2+ or 5V == Binary 1.

Digital Signals and Timing Diagrams

• An ideal digital waveform is a square wave.

Boolean Constants and variables

• Boolean algebra contains 2 values, 0 and 1
• Boolean variable: quantity equal to 0/1
• Voltage is voltage, 0/1 (Logic Level).
• 0/1, Low/High, False/True, Off/On are Synonyms.

Boolean Values

• Boolean algebra: means to expresses relationship with a logic circuit
• Logic Operations: AND / OR/ NOT

OR Gates

• If A or B or both are one
• If not 1
• The same holds for multiline combinations

And Gates

• Can only be 1 when they are all 1

Not gates

• Not is when it is always inverted

The Universal Gates

• NOR and NAND gates can both form an inverter, OR gate or AND gate

Buffers

• Buffer : Where output feeds to next input, the inverters cancel each other
• Used mainly for impedance matching

Inverters in Circuits

• Output is simple input expression
• The overbar represents not operation

Logic Waveform Example Problems

• To be able to understand the operation of components
• To comprehend the language the components use
• Important for signal integrity and digital electronics

Electrical Circuit Logic Examples

• Circuits all form basic and and or relationship for operation

Flip-Flops and Latches

• Flip-flops arrange logic gates and stores binary data

Flip-Flops

• One of interesting thing with using Logic gate is memory. With logic gates, flip flop circuits can be achieved by creating a "remembered" arrangement and maintains the state until altered.

Common Applications for FlipFlops

• The most common application of flip flops,

• Frequency divider circuits

NAND S-R FlipFlops and RS latch

• Constructed within circuits

SR Flip Flops

• Invalid state means states are reverse

The term invalid or determinate

• Is in some cases what the flip-flops and switch reverse or be in same state.

Aperiodic Mode

• data is direct result of discrete events
• updated at a non uniform rate

ARINC 429 standard

• installs standard

• Electrical Characteristic has different variable value

• high performance

Learn the steps to convert a decimal number to its binary equivalent, starting with finding the largest power of 2. Understand how to annotate powers of 2 and determine the binary representation.