🔌Intro to Electrical Engineering Unit 16 – Sequential Logic Circuits

Key Concepts and Definitions

• Sequential logic circuits outputs depend on both current inputs and previous state
• Flip-flops and latches fundamental building blocks of sequential logic circuits
• Registers temporary storage devices that hold multiple bits of data
• Counters special types of registers that increment or decrement their value based on clock pulses
• State machines abstract models that define a system's behavior using states and transitions
• Timing and clock signals synchronize the operation of sequential logic circuits
• Setup time minimum time before the clock edge that input data must be stable
• Hold time minimum time after the clock edge that input data must remain stable

Sequential vs. Combinational Logic

• Combinational logic circuits outputs depend solely on current inputs
  • Examples: AND, OR, NOT, and XOR gates
• Sequential logic circuits outputs depend on both current inputs and previous state
  • Examples: flip-flops, latches, registers, and counters
• Feedback paths in sequential logic circuits allow the output to depend on previous states
• Memory elements (flip-flops and latches) store the previous state in sequential logic circuits
• Combinational logic circuits are memoryless and do not require clock signals
• Sequential logic circuits require clock signals to synchronize the operation of memory elements

Flip-Flops and Latches

• Flip-flops and latches are the basic memory elements in sequential logic circuits
• Latches are level-triggered devices that change state based on the level of the control signal
  • SR latch: Set-Reset latch with two inputs (S and R) and two outputs (Q and Q')
  • D latch: Data latch with one input (D) and one output (Q)
• Flip-flops are edge-triggered devices that change state on the rising or falling edge of the clock signal
  • D flip-flop: Data flip-flop with one input (D) and one output (Q)
  • JK flip-flop: Jack-Kilby flip-flop with two inputs (J and K) and two outputs (Q and Q')
  • T flip-flop: Toggle flip-flop with one input (T) and one output (Q)
• Master-slave flip-flops consist of two latches connected in series to avoid metastability issues
• Flip-flops and latches are used to build more complex sequential circuits like registers and counters

Registers and Counters

• Registers are temporary storage devices that hold multiple bits of data
  • Parallel-in, parallel-out (PIPO) registers load and output data simultaneously
  • Serial-in, serial-out (SISO) registers load and output data one bit at a time
  • Shift registers move data in a specific direction (left or right) with each clock pulse
• Counters are special types of registers that increment or decrement their value based on clock pulses
  • Synchronous counters update their value on the rising or falling edge of the clock signal
  • Asynchronous (ripple) counters propagate the clock signal through a series of flip-flops
  • Up counters increment their value with each clock pulse
  • Down counters decrement their value with each clock pulse
  • Modulo-n counters count from 0 to n-1 and then reset to 0
• Registers and counters are used in various applications, such as data storage, frequency division, and sequence generation

State Machines

• State machines are abstract models that define a system's behavior using states and transitions
• Mealy machines outputs depend on both the current state and the inputs
• Moore machines outputs depend only on the current state
• State transition diagrams visually represent the states and transitions of a state machine
  • Circles represent states, and arrows represent transitions between states
  • Inputs and outputs are labeled on the transitions (Mealy) or states (Moore)
• State transition tables describe the next state and output based on the current state and input
• Finite state machines (FSMs) have a finite number of states and are commonly used in sequential logic design
• State machines are used in various applications, such as control systems, communication protocols, and digital design

Timing and Clock Signals

• Timing and clock signals synchronize the operation of sequential logic circuits
• Clock signals are periodic square waves that oscillate between high and low levels
  • Rising edge: transition from low to high
  • Falling edge: transition from high to low
• Clock period (T) is the time between two consecutive rising (or falling) edges
• Clock frequency (f) is the reciprocal of the clock period (f = 1/T)
• Setup time (tsu) is the minimum time before the clock edge that input data must be stable
• Hold time (th) is the minimum time after the clock edge that input data must remain stable
• Propagation delay (tpd) is the time it takes for a change in input to reflect in the output
• Timing constraints (setup and hold times) must be met to ensure proper operation of sequential circuits
• Clock skew is the difference in arrival times of the clock signal at different parts of the circuit

Design and Analysis Techniques

• State reduction techniques minimize the number of states in a state machine
  • Partitioning: dividing the states into equivalence classes based on output and next-state behavior
  • Implication chart: identifying redundant states that can be merged
• State assignment techniques assign binary codes to the states of a state machine
  • Binary encoding: assigning binary codes in sequence (e.g., 00, 01, 10, 11)
  • Gray encoding: assigning binary codes that differ by only one bit between adjacent states
  • One-hot encoding: assigning a unique bit to each state (e.g., 001, 010, 100)
• Excitation tables determine the input values needed to transition between states in a flip-flop
• Karnaugh maps (K-maps) are graphical tools used to simplify Boolean expressions
• Timing analysis verifies that the circuit meets the required timing constraints
  • Critical path: the longest path between two flip-flops or from input to output
  • Maximum clock frequency: determined by the propagation delay of the critical path
• Verification techniques, such as simulation and formal verification, ensure the correct functionality of the designed circuit

Real-World Applications

• Sequence detectors recognize specific patterns in a stream of input data
  • Example: Detecting the sequence "1101" in a serial data stream
• Frequency dividers generate lower-frequency clock signals from a higher-frequency input clock
  • Example: Dividing a 100 MHz clock by 10 to obtain a 10 MHz clock
• Finite state machines (FSMs) control the operation of various digital systems
  • Example: Traffic light controller with states like "Red," "Yellow," and "Green"
• Shift registers are used in serial communication protocols and data processing applications
  • Example: Converting parallel data to serial data for transmission (PISO)
• Counters are used in timers, frequency synthesis, and event counting applications
  • Example: A 24-hour digital clock using a modulo-60 counter for minutes and a modulo-24 counter for hours
• Synchronous design techniques are used in complex digital systems to avoid timing issues
  • Example: Pipelining in microprocessors to increase throughput and performance
• Sequential logic circuits are essential in various fields, such as computer architecture, digital signal processing, and telecommunications
  • Example: Implementing the control unit of a microprocessor using a finite state machine