Sequential and Combinational Circuits

• Digital circuits' input-output relationship is shown as a truth table.
• High-level circuits use standard logic gates, while low-level representations use electronic switches (transistors).
• Digital systems consist of combinational and sequential systems.
• The output of combinational systems depends only on current inputs.
• The outputs of sequential systems depend on past and present inputs to produce a sequence of operations.
• Simplified representations of sequential system behavior are called state machines.
• Sequential systems divide into synchronous and asynchronous types.
• Synchronous systems change state with a clock signal.
• Asynchronous systems propagate changes when inputs change.
• Synchronous systems use flip-flops to store inputted voltages as a bit when the clock changes.
• Implementing a synchronous sequential state machine involves combinational logic and a state register, representing the state as a binary number.
• The combinational logic produces the binary representation for the next state.
• The clock rate is limited by the most time-consuming logic calculation in the combinational logic.
• Sequential circuits output values based on current and previous input values, using internal memory to store information.
• Examples of sequential circuits: registers, counters, flip-flops.
• Sequential circuits can be used for state machines, timers, counters, and memory elements.
• Sequential circuits store and use previous state information to determine the next state.
• Finite state machines and synchronous sequential circuits are two types of sequential circuits.
• Sequential circuits output based on current and previous input variables. -Memory elements store binary information, and latches store one bit of information.
• Asynchronous sequential circuits use input pulses without a clock signal, ideal for high-speed applications.
• Synchronous sequential circuits use clock signals and level inputs, slower than asynchronous circuits.
• Synchronous sequential circuits are utilized in counters, registers, RAM, MOORE/MEALY state management machines, and other state retaining machines.
• Advantages of synchronous sequential circuits include: memory, timing, state machine implementation, error detection.
• Disadvantages of synchronous sequential circuits: complexity, timing constraints, testing and debugging.
• Flip-flops store binary data and have two stable states with different working types.

Gated SR Latch

• It has three inputs: Set, Reset, and Enable.
• Activated by an ENABLE input that enables the SET and RESET inputs.

Gated D Latch

• It's a gated latch with two inputs: DATA and ENABLE.
• It is designed using a gated SR latch and connected using an inverter.

Master-Slave Edge Triggered Flip-Flops

• "JK Flip Flop": introduces a race-round condition where inputs and CLK are set to 1 for a long time, causing uncertain or unreliable output.
• The master-slave flip-flop has two JK flip-flops in series, the first as the master and the second as the slave, plus an inverter or NOT gate.
• The slave flip-flop is isolated until the clock pulse is true, when its state is affected by inputs J and K.
• When inputs J and K are 1, the master flip-flop works as reset, and the slave flip-flop toggles on the clock's negative transition.

T Flip-Flop

• A type of JK flip-flop with a single input and clock input, with both JK flip-flop inputs connected. Also known as Toggle flip-flop and can find the complement of its state.

JK Flip-Flop

• Improves the S-R flip-flop, resulting in accurate output when S and R input is true by modifying the SR flip flop.
• Adjusts its output Y, functioning as a digital system's Set or Reset Flip-flop, based on the difference in inputs.

Excitation Tables

• Derived from the truth table, consisting of columns for present and next states, and each input.
• They depend on the type of flip-flop.

SR Flip-Flop

• A sequential circuit with two inputs (S for Set and R for Reset) and two outputs (Q and Q').
• It has an excitation table describing required input conditions.

JK Flip-Flop

• A sequential circuit with two inputs (J and K) and two outputs (Q and Q').
• It has an excitation table describing the necessary input conditions for transitioning between states

-Excitation tables are crucial in sequential circuit design. -Ensuring intended state transitions and avoiding race conditions or undefined states.

• It helps maintain circuit stability and functionality.

Registers

• Registers are essential data storage elements in digital electronics.
• They store binary data and holding intermediate results during operations.
• Registers execute machine instructions, manage data, and contribute to system performance.
• Registers are used to store binary data, typically in the form of binary numbers.
• Data can represent values, addresses, instructions, or intermediate results generated during computations.
• Registers are the fastest storage elements in a computer system.
• Registers are located within the CPU, making them easily accessible.
• There come in various sizes, including 8-bit, 16-bit, 32-bit, and 64-bit, depending on the architecture of the processor.
• Different types of registers serve specific purposes, such as general and special-purpose registers and control registers.
• Accumulators are used for arithmetic and logical operations.
• Counters are used for counting.
• Program Counter (PC): Stores the address of the next instruction to be fetched and executed.
• Memory Address Register (MAR): Holds the address of the memory location to read from or write to.
• Memory Buffer Register (MBR): Temporarily stores data read from or to be written to memory.
• Instruction Execution: During the execution of machine instructions, data may be loaded into registers, manipulated in registers, and then stored back in memory or used as operands for subsequent instructions.
• Data Transfer: facilitate data transfer between different components of a computer system, acting as temporary storage buffers for data movement.
• Parallelism: Modern processors use enable parallel processing, allowing multiple instructions to be executed simultaneously or in stages.
• Register File: a collection of registers that can be read from and written to, providing fast and efficient means of accessing and storing data.
• Context Switching: Registers are saved and restored during context switching, to maintain the state of a task.

Counters

• Counters are digital circuits, contributing to functionality and control in both simple and complex systems.
• Asynchronous counters use multiple flip-flops to count events or states, and counting is asynchronous.
• Synchronous counters use a common clock signal to update all flip-flops, suitable for precise timing.
• Up counters increment the count value as events occur.
• Down counters decrement the count value as events occur.
• Binary counters count in binary form, most commonly used.
• Binary-Coded Decimal (BCD) counters count in binary-coded decimal form, for direct decimal counting and display.
• Frequency Counters: measure the frequency of input signals.
• Timer and Delay Generators: Used in timing and generating precise time delays.
• Programmable Dividers: Used to divide a clock signal by a value.
• Address Generation: Counters are used to generate memory addresses for data retrieval and storage.
• Sequence Control: Used in sequence control systems to generate patterns, sequences, or control signals.
• Pulse and Event Counting: Used to count pulses, events, or occurrences.

Verilog Code for Flip-Flops

• Verilog code examples for D, JK, and T flip-flops can be instantiated in Verilog designs.
• Connecting clock signal, data inputs, and outputs, and simulating or synthesizing as needed.
• These examples provide RTL (Register-Transfer Level) descriptions of these flip-flops.
• A D flip-flop, also known as a Data or Delay flip-flop, stores one bit of data and is sensitive to the clock edge, as demonstrated in a Verilog implementation. D Flip Flop Syntax

module d_flip_flop (
input wire clk, // Clock input
input wire d, // Data input
output wire q // Output
); always @(posedge clk) begin
q <= d;
end
endmodule

• A JK flip-flop is a Verilog implementation that stores one bit of data and has two inputs (J and K) for data input and control. JK Flip Flop Syntax

module jk_flip_flop (
input wire clk, // Clock input
input wire j, // Jinput
input wire k, // K input
output wire q // Output
); reg q_next;
always @(posedge clk) begin
if (j && k)
q_next <= ~q; // Toggle state
else if (j)
Syntax
q_next <= 1'b1;
else if (k)
q_next <= 1'b0;
end
always @(posedge clk) begin
q <= q_next;
end
endmodule

• A T flip-flop, also known as a Toggle flip-flop, is a Verilog implementation that toggles its output

Explore the functionalities of sequential and combinational circuits. Sequential circuits use previous state info. Synchronous sequential circuits use a clock signal, ideal for counters, registers, and state management. Gated SR Latches and D latches are also covered.