Digital Logic Designs

LECTURE # 10

STATE MACHINES

• What is a State Machine?
• A state machine (also called a Finite State Machine or FSM) as a mathematical model of computation that consists of:
• A finite set of states.
• A set of inputs.
• A set of outputs.
• Transition functions that determine the next state based on the current state and input.
• Output functions that determine the output based on the current state (Mealy) or the current state and input (Moore).
• State machines are sequential circuits – their output depends on past inputs as well as the current input.

• Why are State Machines Important?
• State machines are designing sequential digital systems. They provide a structured way to design complex control logic.
• Key applications:
• Controllers for digital systems (e.g., vending machines, traffic lights, elevator controllers).
• Protocol implementations (e.g., communication protocols).
• Pattern recognition.
• Game logic.
• Hardware description languages (HDLs) often use state machines as a fundamental building block.

• Types of State Machines
• The two main types of state machines:
• Moore Machines: Output depends only on the current state.
• Mealy Machines: Output depends on both the current state and the current input.

�Programmable Logic Devices

• The Need for Programmable Logic:
• Traditional digital circuit design using discrete logic gates (AND, OR, NOT, etc.).
• The limitations of discrete logic:
• Inflexibility: Hardwired logic; changes require rewiring.
• Complexity: Large designs require many components and complex wiring.
• Space and Power: Discrete components consume significant space and power.
• Introduce PLDs as a solution to these limitations: devices that can be configured to implement a wide variety of digital circuits.

I. Programmable Logic Devices (PLDs)

• PLDs are integrated circuits that contain an array of logic gates that can be configured by the user to implement specific digital functions.
• Aspects of programmable: The logic function is not fixed at the time of manufacture but can be customized by the designer.
• Advantages of Using PLDs:
• Flexibility: Circuits can be easily modified and reconfigured without rewiring.
• Reduced Complexity: Fewer components, simpler board layout.
• Faster Design Cycles: Design changes can be implemented quickly in software.
• Lower Cost (in many cases): Especially for complex designs or when changes are expected.
• Space and Power Savings: Higher integration leads to smaller, more power-efficient designs.

• Types of PLDs:
• The main categories of PLDs:
• Simple PLDs (SPLDs): PROM, PAL, PLA
• Complex PLDs (CPLDs)
• Field-Programmable Gate Arrays (FPGAs)

. Simple Programmable Logic Devices (SPLDs)

• General Architecture:
• Basic architecture common to most SPLDs:
• An array of AND gates.
• An array of OR gates.
• Programmable connections between the inputs, AND gates, and OR gates.

• PROM (Programmable Read-Only Memory):
• Architecture of a PROM:
• Fixed AND array (decoder).
• Programmable OR array.
• PROM can be used to implement combinational logic functions: the address lines are the inputs, and the data lines are the outputs.
• PROMs are primarily used for memory applications, but can also implement simple logic functions.
• PAL (Programmable Array Logic):
• Programmable AND array.
• Fixed OR array.
• PAL provides more flexibility than a PROM for implementing logic functions because the AND array is programmable.
• PAL can implement multiple sum-of-products (SOP) expressions.

• PLA (Programmable Logic Array):
• Programmable AND array.
• Programmable OR array.
• PLA provides the most flexibility of the three SPLDs because both the AND and OR arrays are programmable. This allows for more efficient implementation of complex logic functions.
• PLAs are generally more complex and expensive to manufacture than PALs, so they are less commonly used.

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III. Complex Programmable Logic Devices (CPLDs)

• Limitations of SPLDs:
• SPLDs are limited in the complexity of the circuits they can implement due to their relatively small size and fixed architecture.

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• Architecture of CPLDs:
• Multiple SPLD-like blocks (logic blocks or macro_cells).
• A programmable interconnect matrix (switch matrix) that connects the logic blocks.
• I/O blocks for connecting to external circuits.
• Logic Blocks/Macrocells:
• A programmable AND-OR array (similar to a PAL or PLA).
• Flip-flops for implementing sequential logic.
• Multiplexers for selecting different functions or feedback paths.
• Interconnect Matrix:
• The interconnect matrix allows any logic block to be connected to any other logic block or to the I/O pins.
• This provides a high degree of flexibility for implementing complex circuits that span multiple logic blocks.

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• Advantages of CPLDs:
• Higher Capacity: Can implement larger and more complex circuits than SPLDs.
• Increased Flexibility: The programmable interconnect matrix allows for complex routing.
• Good Performance: CPLDs typically offer good performance for a wide range of applications.
• Non-Volatile: Configuration is typically stored in non-volatile memory (e.g., EEPROM or flash memory), so the device retains its configuration when power is removed.
• Applications of CPLDs:
• Glue logic: Interfacing between different components in a system.
• Address decoding.
• Simple state machines and controllers.
• Peripheral control.

IV. Field-Programmable Gate Arrays (FPGAs)

• Limitations of CPLDs:
• CPLDs, while more powerful than SPLDs, still have limitations in terms of capacity, flexibility, and performance for very complex designs.
• Architecture of FPGAs:
• A large array of configurable logic blocks (CLBs).
• A programmable interconnect network that connects the CLBs(Configurable logic blocks).
• I/O blocks for connecting to external circuits.
• Configurable Logic Blocks (CLBs):
• Lookup tables (LUTs) for implementing combinational logic functions.
• Flip-flops for implementing sequential logic.
• Multiplexers for selecting different functions and routing signals.

• Interconnect Network:
• The interconnect network consists of a hierarchy of programmable switches and routing channels that allow any CLB to be connected to any other CLB or to the I/O pins.
• This provides a very high degree of flexibility for implementing complex routing and signal distribution.
• Advantages of FPGAs:
• Very High Capacity: Can implement extremely large and complex circuits.
• Maximum Flexibility: The fine-grained architecture and highly programmable interconnect network provide unparalleled flexibility.
• High Performance: FPGAs can achieve very high performance, especially for custom hardware accelerators.
• Reconfigurable: FPGAs can be reconfigured dynamically, allowing for adaptive hardware and rapid prototyping.

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• Disadvantages of FPGAs:
• More Complex Design Process: Designing for FPGAs requires specialized tools and expertise.
• Higher Power Consumption: FPGAs typically consume more power than CPLDs.
• Volatile Configuration: Most FPGAs use SRAM to store the configuration, so the configuration is lost when power is removed (requires an external configuration memory). Some FPGAs use flash memory for non-volatile configuration.
• Applications of FPGAs:
• Digital signal processing (DSP).
• Image and video processing.
• Networking and communications.
• Embedded systems.
• Hardware acceleration.
• Rapid prototyping of ASICs (Application-Specific Integrated Circuits).

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V. PLD Selection and Design Flow

• Choosing the Right PLD:
• Complexity of the design.
• Performance requirements.
• Power consumption.
• Cost.
• Availability of development tools and support.

General guidelines:

• SPLDs: For very simple logic functions and glue logic.
• CPLDs: For medium-complexity designs, address decoding, and control logic.
• FPGAs: For high-complexity designs, DSP(digital signal processor), hardware acceleration, and applications requiring maximum flexibility.

The End