B1-05.05 LOGIC CIRCUITS

Logic Circuits (5.5) Learning Objectives:

• Identification of common logic gate symbols, tables, and equivalent circuits.
• Description of the applications of logic circuits used in aircraft systems and schematic diagrams.
• Interpretation and understanding of logic diagrams.
• Description of the operation and use of latches and clocked flip-flop logic circuitry.

Boolean Logic:

• Information that is being processed in digital systems is usually present in binary form.
• Devices with two operating states can represent binary quantities.
• A switch represents a binary state: open (0) or closed (1).
• Punched holes (1) or the absence of holes (0) can represent binary numbers.
• Numerous devices have two operating states or can be operated in two extreme conditions.
• Binary information is represented by voltages (or currents) in electronic digital systems.
• Binary 0 and 1 are represented by two nominal voltage levels.
• Any voltage between 0 and 0.8 V = 0 and any voltage between 2 and 5 V = 1, so input and output signals normally fall within one of these ranges.
• The exact voltage's value is not important in digital systems, unlike analogue systems.

Digital Signals and Timing Diagrams:

• A timing diagram represents a digital signal and its variation over time
• The horizontal time scale is marked off at intervals, starting at t0.
• Signals maintain a given voltage/binary state until a time and transition (jump) to another.
• Transitions are represented as vertical lines on timing diagrams, although they aren't instantaneous in reality.
• 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 are compared through expected timing diagrams on an oscilloscope or logic analyser, which is essential for testing & troubleshooting procedures.

Boolean Constants and Variables:

• Boolean algebra differs from ordinary algebra.
• Boolean constants and variables can only have two values: 0 or 1.
• Boolean variables are used to represent the voltage level on a wire or at the I/O terminals of a circuit.
• Boolean 0 may be assigned to any voltage from 0 to 0.8 V, while Boolean 1 is a voltage from 2 to 5 V.
• Boolean 0 and 1 represent the state, called logic level, of a voltage variable.
• A voltage in a digital circuit can be at the logic 0 level or the logic 1 level, depending on its actual value.
• Letter symbols represent logic variables, for example, A represents an input or output with a value of either 0 or 1.
• Boolean algebra is easier because only two values are possible and excludes fractions and decimals.
• Boolean algebra has 3 basic operations: AND, OR, and NOT

AND, OR, and NOT Operations:

• These basic operations are called logic operations.
• Digital circuits can be constructed from diodes, transistors, and resistors connected in such a way to produce an output based on logic operations.
• Logic gates can then be used to analyze and design combinations of logic gates connected as logic circuits.

Truth Tables:

• Tables that show a logic circuits output depending on the logic levels present at the circuits inputs.
• They list all possible combinations of logic levels present at inputs, along with the corresponding output level.
• For an N input truth table, the number of input combinations equals 2^N.
• The list of all possible input combinations follows the binary counting sequence.

Simple Logic Gates:

• A logic gate represents a physical electronic device that implements boolean logic
• Combinations of logic gates create logic circuits, which are used in electronic devices, creating integrated circuits and microprocessors.
• Logic gates are the building blocks of all logic circuits.
• All logic actions can be analyzed & simplified into basic actions such as OR, AND, and NOT gates.

OR Gates:

• The OR operation is a basic Boolean operation.
• Shows what happens when two logic inputs (A, B) are combined using the OR operation to produce an output (X).
• Output is logic 1 for every combination where one or more inputs are 1
• Output is 0 when both inputs are 0.
• X = A + B is the Boolean expression for OR operation. The "+" sign stands for the OR operation.
• The OR operation produces 1 + 1 = 1, not 1 + 1 = 2.

AND Gates:

• The AND operation is the second basic boolean operation
• A and B are combined using the AND operation to produce output X
• X is a logic 1 only when both A and B are at the logic 1 level - Output is 0 when one of the inputs is 0.
• Boolean expression for the AND operation is: X = A.B
• The "." sign stands for the Boolean AND operation and operates the same as in ordinary multiplication
• "X equals A AND B" means that X will be 1 only when A and B are both 1, which can be shortened to X = AB

NOT Gate, or Inverter:

• The NOT operation can be performed on a single input variable
• The input, A, subjected to the NOT operation gives a result of X.
• A an inverter.
• Where the over-bar represents the NOT operation, read as 'X equals NOT A' or 'X equals the inverse of A' or 'x equals the complement of A'.
• Common usage to show that the logic value is:
  • X = A (the output) is opposite to the logic value of A (the input).
  • A clarifies this.
  • When A = 0, X = A, the output, is the opposite; therefore it has to be equal to 1
  • Conversely, when A = 1, X = A, the output, is the opposite; therefore it has to be equal to 0 Multiple input gates can be constructed placing gates in special configurations

Inverters in Circuits:

• An output expression is simply equal to the input expression with a bar over it in the diagram
• An inverted value in text will be referred to as A_bar if the variable is A
• Equation for the circuit on the left is : A_bar + B (A is inverted and then ORed with B)
• X = A + B Equation for the circuit on the right (shows A or B and X equals the inverse of (A OR B).
• A + B ≠ A + B

Compound Logic Gates

NOR Gate:

• Like an OR gate, but with a small circle on the output.
• The small circle indicates the inversion operation.
• Operates as an OR gate followed by an inverter
• Truth Table shows the NOR gate output is the exact inverse of the OR gate output for all possible input conditions.
• OR gate output goes HIGH when any input is HIGH
• NOR gate output goes LOW when any input is HIGH.
• This same operation can be extended to NOR gates with more than two inputs.

NAND Gate:

• Like the AND gate, but with a small circle on its output to denote the inversion operation.
  • The output is the same as an AND gate with a bar over all the inputs
  • Truth Table shows the NAND gate output is the exact inverse of the AND gate for all possible input conditions.
  • AND output goes HIGH only when all inputs are HIGH
  • NAND output goes LOW only when all inputs are HIGH; characteristic is true of NAND gates having more than two inputs.

Exclusive-OR (XOR):

• If the input is either A or B it returns 1. If the input is both A and B it returns O, and if the input is neither A or B it returns O.
• Truth Table shows that X = 1 for the two cases where inputs are equal to:
  • A = 0 and B = 1
  • A = 1 and B = 0
• Produces a HIGH whenever the two inputs are at opposite levels
  • Abbreviated to XOR
• X = A.B + A.B and (Ā. B) + (A. B) = 1

Exclusive-NOR (XNOR):

• Operates completely opposite to the XOR circuit.
• A HIGH output is produced whenever the two inputs are at the same level.
• X = (A AND B) + (NOT A AND NOT B)

Universal Gates:

• The NOR gate and the NAND gate can be considered universal gates: combinations can accomplish any of the basic operations.
• The non-inverting gates are versatile, because they can produce an invert

Buffers:

• Connecting two inverters cancels each other out results a buffer.
• Useful as an impedance-matching device, it operates slightly different depending on the type such as a voltage buffer or current buffer
• In logic circuits, the buffer is a single-input device with a gain of 1, mirroring the input at the output.

Flip-Flops and Latches

Flip-Flops:

• An arrangement of logic gates that will remember an input value
• Maintains a state (1 or 0), until directed to change its state Historically, transistor versions of these circuits were common in computers Made from logic gates now with various forms
• They do the following:
  • Counters
  • Registers
  • Frequency Divider circuits -Data transfer

Flip-Flops:

• With two stable states; used to store state information or a single bit of binary data
• Basic operation: application of a pulse at one input, causes it to flip into one of its two stable states and remain latched in that state.
• A pulse at the other input causes it to 'flop' into the other state
• The two output terminals are designated Q and Q bar to mean invert, so read Not Q, referenced as Q'
• Flip-flop is made up of a latch circuit with an S-R flip-flop making use of the S-R latch logic circuit and a clock to complete the device.

Flip-Flops Circuits Include:

• Set-Reset (SR) flip-flop
• Master-Slave (JK) flip-flop
• Data (D) flip-flop
• Toggle (T) flip-flop.

NAND Gate S-R Flip-Flops:

• A simple flip-flop built using two NAND gates

• Fundamental operation is based on the SR flip-flop diagram

• S is Set

• R is Reset -Q is output gate 1

• Q' is output gate 2

• Referred to as an S-R latch with outputs that "latch" to either 1 or 0 based on a pulsed input

• Gates can vary for other latch circuits than NAND

• The term invalid condition means that for the inputs shown, the flip-flops may switch to reverse the output states, or they may remain in an existing condition

S-R Latch Operation (NAND):

• Latch will be in an invalid state with high outputs when pulsed low for set and reset
• Use of NAND gates ensures that it will be at rest when both inputs are high

Regular Operations of Set and Reset:

• Pulse low and will be expected to do the opposite of their named roles (resting)
• When pulsed low, reset will be performed, since S-R flip-flop is at high S-R Flip Flops will be resting in HIGH state since an input here changes any outputs

Summary of a Flip-Flop

• A way to store a single bit of data (binary)
• Application of a pulse causes a flip into a stable state, or flop into another state previously Terminals are Q and Q"
• State is either normal, referred to as complement logic, normal logic or complement logic.
• Latching has applications for memory

NOR Gate S-R Flip-Flops:

• Basic Flip-Flop can constructed using NOR gates
• Works in reverse from normal latch operations

Setting and Clearing the S-R Latch:

• When Set input is momentarily pulsed low and Clear is kept high, Q will latch to a high or 1 with Q' at 0.
• If the Set is low, or low again, the process is still unaffected and the set is the end result:
  • Low Pulse on Set will set the latch/ flip-flop To clear the latch, Reset is pulsed high while Set remains low: Q goes low with resets.
  • Held at 0 by a 1 applied to the top gate's input.
  • High Pulse on Reset input resets the state

Alternate Representations:

NAND: when pulsed low, the flip -flop gets triggered (Active Low gates/Input)

Active Highs:

When pulsed high triggers the state of operation

• S and R are held low NOR gates Inputs will have reversed characteristics

Flip-Flop Invalid and Initial States:

• The two inputs are pulsed low

• When the inputs are used, states reverse

On Startup:

Depending on the invalid and starting state, the output is determined by the load, delay, propagation

S-R Flip-Flop Practical Usage:

Virtually impossible to not have bounces from mechanic activation: will not have a clean operation

De-Bounce for operations:

Need a latch so that it will prevent extra signals from affecting output

Counter Shift Resisters:

Must be in sync so that there are no clock-like operations