B1-05.05 LOGIC CIRCUITS

Logic Circuits (5.5) Learning Objectives

• Common logic gate symbols, tables, and equivalent circuits can be identified.
• Applications of logic circuits used in aircraft systems and schematic diagrams can be described.
• Logic diagrams can be interpreted and understood.
• The operation and use of latches and clocked flip-flop logic circuitry can be described.

Boolean Logic

• Information is usually in binary form in digital systems
• Devices with two operating states represent binary quantities

Representing Binary Quantities

• A switch has two states: open or closed
• An open switch can represent binary 0, and a closed switch can represent binary 1.
• Holes punched in paper used to represent binary numbers
• A punched hole is a binary 1
• The absence of a hole is a binary 0.
• Binary information is represented by voltages or currents at inputs/outputs in electronic digital systems
• Binary 0 and 1 typically have two nominal voltage levels
• 0 V may represent binary 0, and +5 V may represent binary 1
• Circuit variations mean 0 and 1 are represented by voltage ranges
• Voltages between 0 and 0.8 V represents 0
• Voltages between 2 and 5 V represents 1.
• Signals fall in range, except during transitions.

TTL Voltage Levels

• Exact voltage isn't important in digital systems
• 3.6 V means the same as 4.3 V
• Exact voltage is important in analogue systems
• 3.6 V represents a different temperature compared to 4.3 V.
• Analogue circuitry design is more difficult because exact values are affected by component variations, temperature, and noise.

Digital Signals and Timing Diagrams

• A typical digital signal and its variation over time is a graph of voltage versus time (t), called a timing diagram
• The horizontal time scale is marked off at regular intervals, beginning at to and proceeding to t1, t2
• Signal starts at 0 V (binary 0) at time to in timing diagram
• It remains there until time t1
• At t1, the signal makes a rapid transition (jump) up to 4 V (binary 1).
• At t2, the signal jumps back down to 0 V.
• Similar transitions occur at t3 and t5.
• The signal remains at 4 V from t3 to t5.
• Transitions on the timing diagram are drawn as vertical lines, so they appear instantaneous
• It's necessary to show the transitions more accurately on an expanded time scale in some situations
• Timing diagrams show how digital signals change with time.
• They show the relationship between two or more digital signals in the same circuit or system
• Signals can be compared to expected timing diagrams using an oscilloscope or logic analyzer
• It's an essential part of testing and troubleshooting in digital systems.

Boolean Constants and Variables

• Boolean algebra differs from ordinary algebra, in that Boolean constants and variables have only two possible values: 0 or 1
• A Boolean variable is a quantity that may be equal to either 0 or 1 at different times
• Boolean variables often represent the voltage level present on a wire or at the I/O terminals of a circuit
• Boolean value of O might be assigned to any voltage from 0 to 0.8 V, while the Boolean value of 1 is to any voltage from 2 to 5 V in a digital system.
• Boolean 0 and 1 represent the state of a voltage variable, or its logic level
• A voltage in a digital circuit has either a logic 0 level or a logic 1 level, depending on its numerical value
• In digital logic, other terms are used synonymously with 0 and 1
• The 0/1 and LOW/HIGH designations are commonly used
• Boolean algebra expresses the relationship between a logic circuit's inputs and outputs
• Inputs are logic variables whose logic levels determine output levels
• Letter symbols represent logic variables
• If the letter A represents a digital input or output, then A = 0 or A = 1.

Boolean Values

• Boolean algebra is easy to work with due to the two possible values
• Boolean algebra doesn't use fractions, decimals, negative numbers, square roots, cube roots, logarithms, or imaginary numbers
• There are only three basic operations in Boolean algebra: AND, OR, and NOT

AND, OR and NOT

• Logic operations are made up of Digital circuits (logic gates)
• Logic gates are constructed from diodes, transistors, and resistors
• The circuit output is the result of a basic logic operation (OR, AND, NOT) performed on the inputs.
• Boolean algebra describes and analyzes basic logic gates, and then analyzes and designs combinations of connected logic gates.

Truth Tables

• Truth table describes how a logic circuit's output depends on the logic levels present at the circuit's inputs
• Lists all logic level combinations at inputs A and B with corresponding output level X
• Shows the output state for any set of input conditions.
• Two-input truth table has four entries
• Three-input has eight entries
• Four-input has 16 entries
• The number of input combinations will equal 2N for an N input truth table.
• The list of all possible input combinations follows the binary counting sequence

Simple Logic Gates

• A logic gate is an ideal representation of electronic device that implements boolean logic
• A combination of logic gates creates a logic circuit
• Logic circuits create integrated circuits and microprocessors in electronic devices
• Logic circuits combine many logic gates
• Complex logic circuits assemble from simpler ones, which assemble from gates
• The building block of logic circuits is the logic gate
• Logic actions can be analyzed and simplified into basic actions that are OR gates, AND gates and NOT gates

OR Gates

• The OR operation is the first basic boolean operation
• The truth table shows when two logic inputs, A and B, are combined in the OR operation to create any output X
• X is logic 1 for every input level combination where one or more inputs are 1
• X is 0 only when both inputs are 0

OR Gate (2 input)

• With Truth Table
• Boolean expression X = A + B, where the + stands for the OR operation
• The expression is like ordinary addition except when A and B are both 1 (1 + 1 = 1, not 2)
• In boolean algrebra the highest a result can be is 1

OR gates (three input)

• X = A + B + C
• If all three inputs are 1, we have X = 1+1+1 = 1
• The expression X = A + B is read as 'X equals A OR B,' so X will be 1 when A or B or both are 1
• Likewise, the expression X = A + B + C is read as 'X equals A OR B OR C,' so X will be 1 when A or B or C or any them are 1

AND Gates

• The AND operation is the second boolean operation
• The truth table shows inputs A and B combine using the AND operation to produce output X
• X is logic 1 only when both A and B are at the logic 1 level, otherwise the output is 0
• The boolean expression is X = A.B, but "." stands for the boolean AND operation instead of multiplication.

AND Gate

• Operates the same as in ordinary multiplication, helpful in evaluating logic expressions

AND Gate Expression

• The expression X = A.B. C = ABC reads as 'X equals A AND B AND C', so X will be 1 only when A, B and C are all 1.

NOT Gate (Inverter)

• Performs on a single input variable unlike the OR and AND operations
• Subjecting a variable A to the NOT operation gives the result X
• The NOT gate is called an inverter
• The terms 'NOT gate' and 'inverter' are used interchangeably
• X = A is read as 'X equals NOT A' or 'X equals the inverse of A' or 'x equals the complement of A'.
• X = A means that the logic value is opposite to the logic value of A
• X = A applies to A = 0 and A = 1.

Combining Gates

• Multiple input gates can be constructed by placing gates in special configurations
• A three-input AND gate may be constructed using two AND gates connected
• A three-input OR gate may be constructed using two OR gates connected.

Logic Circuits

• No matter how complex, can be completely described using the three basic boolean operations
• The OR gate, AND gate and NOT circuit are the basic building blocks of digital systems

Simple AND/OR Circuits

• Take the example circuit with inputs (A, B, C) and single output (X)
• The AND gate output is written A.B
• AND output connects as input to the OR gate along with C, OR the output as: X = A • B+C

AND/OR Circuits Order of Operations

1. A.B is ORed with C, or
2. A is ANDed with the term B + C.

• If an expression contains both AND and OR operations, the AND operations are performed first unless there are parentheses, making that operation first
• The rule is the same used in ordinary algebra
• Output X = 1 when C is 1; and C is 0 and A + B are both 1

Alternate AND/OR Circuit

• Expression for the OR gate output is simply A + B
• The output serves as an input to the AND gate along with another input, C
• AND gate output is expressed as X = (A + B).C
• Parentheses indicate that A and B are ORed first, before their OR sum is ANDed with C
• Without parentheses would be interpreted incorrectly since A + B.C means A is ORed with the product B.C.

Inverters in Circuits

• The output equals the input expression with a bar over it, e.g. A_bar
• Equation for the circuit (on the left) is A_bar + B
• The bar is over the A alone, indicating that A is first inverted and then ORed with B.
• The output of the OR gate is equal to A + B
• The inverter output is therefore equal to the complete input expression negated.
• X equals the inverse of (A OR B)

Inverter Equations

• Note that in the right circuit, the bar covers the entire expression (A + B), important because, as will be shown later, the following expressions are NOT equal.
• A + B does not equal A + B

Combined Gates

Compound Logic Gates

• The Truth table shows that the NOR two input gate:

NOR Gate

• The NOR gate operates like an OR gate followed by an inverter
• Truth table shows NOR gate output is the exact inverse of the OR gate output for all conditions
• OR gate output goes HIGH when input is HIGH, so NOR gate output goes LOW when any input is HIGH
• The operation can be extended to NOR gates with >2 inputs

NAND Gate Circuit

• Called NAND since it operates like an AND gate followed by an inverter
• The symbol matches an AND gate but with the circle on its output
• A NAND gate is equivalent to an AND followed by a NOT
• The NAND gate truth table is the inverse of the AND for any case. meaning all inputs are HIGH.

Exclusive-OR (XOR)

• If the input is either A or B, output is 1
• If input is both A and B the output is 0; if the input is neither A nor B it returns 0.
• The output of an XOR produces HIGH whenever the two inputs are at opposite levels.
• Exclusive-OR is abbreviated to XOR.

XOR Gate

Exclusive-NOR (XNOR) Circuit

• The XNOR or Exclusive-NOR circuit operates completely opposite to the XOR circuit.
• It produces a HIGH output whenever the two inputs are at the the same level
• Output of the XNOR circuit is the exact inverse of the output of the XOR circuit
• This translates to the symbol for the XNOR gate obtained by simply adding a small circle at the output of the XOR symbol.
• AB + AB

Universal Gates

• The NOR and NAND gates are universal gates
• Combinations of them accomplish any of the basic operations
• Invertors, OR gates, and AND gates can be produced
• The non-inverting gates do not have this versatility

Buffers

• Two inverter gates connected together cancel each other out
• This buffer is useful as an impedance-matching device
• In logic circuits, the buffer is a single-input device which has a gain of 1, mirroring the input at the output
• The common collector amplifier (BJT) is often called an emitter follower used to buffer a voltage source
• An op-amp can be used as a unity gain amplifier called a voltage buffer and has closed-loop closed-loop feedback
• Effective isolation is provided because the input impedance of the op-amp is very high
• Very little power is drawn from the signal source, thus avoiding 'loading' effects
• Voltage followers are used to construct buffers for logic circuits.

Inverting Buffers (Inverters)

• Produces opposite state to the input. High input means low output, and vice versa
• Known as an inverter
• A transistor switch with a collector resistor serves as an inverting buffer
• When the switch is open, zero current flows in the base, so the collector current is cut off
• The resistor RC must drive the transistor to saturation
• The voltage VCC is used to operate the inverting buffer
• The output is taken below the load resistor and can function as an inverting buffer in digital circuits.

IEEE Gate Symbols

• Developed together with the American National Standards Institute (ANSI), the Institute of ANSI electrical and Electronic Engineers (IEEE).
• Revision of standard is ANSI/IEEE Std
• These symbols are widely used

Fabrication of Gates

• Gates are fabricated as IC packs in dual, triple or quadruple circuit arrangements
• The diagram illustrates manufacturer data presentation
• Relates to a quad two-input NAND circuit arrangement within a Dual-In-Line (DIL) pack monolithic IC
• Numbered squares represent the connecting pins.

Application of Logic Circuits in Aircraft Systems

• Shown by using the Emergency Electrical Power Logic (A-320 Example ONLY)
• In A-320
• If AC BUS 1 and 2 are lost above a given airspeed the Ram Air Turbine (RAT) extends automatically
• The RAT is air-driven turbine in an electrical power logic application

Binary data in digital systems is represented in various ways, from switches to voltage levels. Understanding these representations is crucial for comprehending how computers process information. This includes understanding the role of voltage levels, punched cards and other hardware components.