combinatorial logic circuit
Combinational logic circuits are a basic class of circuit types in digital electronics that consist of a series of logic gates used to implement a specific logic function. Unlike temporal logic circuits, the output of a combinational logic circuit depends entirely on the current input signal and is not affected by previous inputs. In other words, combinational logic circuits have no memory function and the output is determined only by the inputs at the current moment.
Basic features of combinational logic circuits:
- non-memorable: The output depends only on the current input state and is independent of past input states.
- Immediate response: The output also responds as soon as the input changes.
- stability: As long as the inputs remain constant, the outputs will also remain constant.
- predictability: For a given input, the output is predictable.
Components:
Combinational logic circuits usually consist of the following basic logic gates:
- with door (AND): The output is high only when all inputs are high.
- Or Gate (OR): As long as any of the inputs is high, the output is high.
- Non-gate (NOT): Inverts the input signal, i.e., a high level becomes a low level and a low level becomes a high level.
- Different-or Gate (XOR): When the input signals are different, the output is high; when the input signals are the same, the output is low.
- Same-or Gate (XNOR): In contrast to an iso-or gate, the output is high when the input signals are the same, and low when the input signals are different.
- NAND: Inverts the output of the gate.
- Non-Response Gate (NOR): The output of the or gate is inverted.
Application Example:
- Adder: Used to perform binary addition operations.
- Encoder: Converts a set of input signals into a corresponding code.
- Decoder: Converts a code into a set of output signals.
- Multiplexer: Selects an output from multiple input signals.
- Demultiplexer: Assigns an input signal to multiple output channels.
- Comparator: Used to compare the size of two numbers.
Design Process:
Designing a combinational logic circuit usually involves the following steps:
- Defining Functions: Define the functional requirements of the circuit.
- truth table: Create a truth table to list all possible combinations of inputs and the corresponding desired outputs.
- boolean expression: Derive a Boolean expression from the truth table.
- simplified expression: Simplify Boolean expressions using Boolean algebra rules.
- logic gate implementation: Convert simplified Boolean expressions into concrete logic gate circuits.
Realization tools:
Modern design processes often use computer-aided design (CAD) tools for circuit design and simulation to ensure that circuits are functionally correct and performance is optimized.
Summary:
Combinatorial logic circuits are the basis of digital circuit design and are widely used in a variety of electronic devices. They are simple, reliable, and capable of efficiently accomplishing specific logic operation tasks.
sequential logic circuit
Temporal logic circuits are another important type of circuit in digital electronics. Unlike combinational logic circuits, temporal logic circuits not only consider the input signals at the current moment, but also determine the output signals based on the state information within the circuit. This means that temporal logic circuits have a memory function that remembers past state information and combines it with the current input to determine the output.
Basic features of timing logic circuits:
- storability: Timing logic circuits contain storage elements (e.g., flip-flops, registers, etc.) that are capable of storing data or state.
- Clock control: The operation of most timing logic circuits is controlled by a clock signal, i.e., the circuit updates its internal state only when a rising or falling edge of the clock signal arrives.
- dynamic behavior: The behavior of a timing logic circuit changes over time, and its output depends not only on the current input signal, but also on the current state within the circuit.
- sophistication: Compared to combinational logic circuits, temporal logic circuits are usually more complex and more complicated to design and analyze.
Components of a timing logic circuit:
Timing logic circuits usually consist of the following components:
- Flip-flops: A basic memory cell that holds one binary bit of information.
- Registers: Consists of multiple triggers for storing multiple bits of data.
- Counters: Capable of incremental or decremental operation depending on the clock signal.
- Finite State Machines (FSMs): An advanced form of temporal logic circuit that determines the next state and the output signal based on the input signal and the current state.
Application Example:
- processor register: Used to temporarily store data, such as general-purpose registers and instruction registers in the CPU.
- register: Used to implement counting functions such as clock counters, address counters, etc.
- finite state machine (FSM): Used to implement complex control logic, such as control units in microprocessors, communication protocol controllers, etc.
Design Process:
Designing a timing logic circuit usually involves the following steps:
- Defining Functions: Define the functional requirements of the circuit.
- state chart: Draw state diagrams to represent the various possible states of a circuit and the transitions between them.
- status code: Assign a binary code to each state.
- equation of state: Derive state equations based on state diagrams and state coding.
- output equation: Derive the output equation based on the state diagram and state coding.
- logic gate implementation: Converts state and output equations into specific logic gate circuits.
Realization tools:
Modern design processes often use hardware description languages (HDL) such as VHDL or Verilog for circuit design and description, and computer-aided design (CAD) tools for simulation, synthesis, and layout and wiring steps.
Summary:
Timing logic circuits are one of the core components of modern digital systems and are widely used in various electronic devices such as microprocessors, memories, and communication systems. They enable circuits to perform complex logic operations at different points in time by storing state information, thus realizing more advanced functions.
Combinational Logic Loop
A Combinational Logic Loop is a misconfiguration that occurs in a digital circuit or logic design in which there is a feedback loop that allows signals to continually loop back to themselves without a clear steady state. This loop usually results in the circuit failing to reach a stable output state, leading to functional errors.
Characterization of combinatorial logic rings:
With the above basics, it is not difficult to understand combinational logic loops
- unstable state: Combinatorial logic circuits are supposed to produce deterministic outputs based on inputs, but when loops exist, the outputs become dependent on previous output states, creating a feedback mechanism that prevents the outputs from stabilizing.
- infinite loop: The signal will continue to circulate inside the loop and theoretically never stop unless external conditions change or the circuit breaks the loop.
- (math.) competitive condition: As signals are constantly circulating within the loop, this may lead to competing conditions, i.e., signals arriving in a different time order, leading to different results.
The reason for the combinatorial logic ring:
- direct connection: Two or more logic gates are directly interconnected to form a loop.
- Indirect formation through external circuitry: While each individual part is correctly combinationally logical, they are connected in such a way as to form a loop.
Methods for avoiding combinatorial logic loops:
- elaboration: Avoid any connection that could form a loop when designing the circuit.
- Using Temporal Logic: If you need to store state or feedback, you should use temporal logic (e.g., triggers) rather than combinatorial logic.
- Verify the design: Use a logic simulation tool to verify that no loops exist in the design.
Example:
Suppose there is a simple combinational logic circuit containing 1 non-gate (NOT gates) whose output is connected to its own input. Such a design constitutes a combinational logic loop, since the output of the non-gate directly affects its input, creating an infinite loop of states whose final state cannot be determined.
Summary:
A combinational logic loop is a circuit design error that usually needs to be avoided. In digital circuit design, it is correct to use timing logic (e.g., flip-flops, registers, etc.) to handle situations where state needs to be stored, rather than allowing combinational logic elements to form loops.