Sequential Circuits
What is Sequential Circuits?
A digital circuit whose output depends on the present inputs and the past sequence of inputs, achieved through the use of memory elements.
Key formula / rule: SR Flip-flop Excitation Table
Key points
- Understand the difference between combinational and sequential circuits.
- Identify and analyze basic memory elements (latches and flip-flops).
- Differentiate between synchronous and asynchronous sequential circuits.
- Analyze state tables and state transition diagrams.
Common exam trap
Confusing synchronous and asynchronous circuit behavior.
Definitions
- Term
Sequential Circuit
- Meaning
A digital circuit whose output depends on the present inputs and the past sequence of inputs, achieved through the use of memory elements.
- Term
Flip-flop
- Meaning
A basic bistable memory element capable of storing one bit of information. It has two outputs, Q and Q', and typically requires a clock signal for state changes.
- Term
State Table
- Meaning
A table that lists all possible states of a sequential circuit, the corresponding inputs, and the next state and output for each combination.
- Term
State Transition Diagram
- Meaning
A graphical representation of a sequential circuit's behavior, showing states as nodes and transitions between states as directed arcs labeled with input/output.
- Term
Synchronous Sequential Circuit
- Meaning
A sequential circuit where all state changes are controlled by a common clock signal, ensuring synchronized operation.
- Term
Asynchronous Sequential Circuit
- Meaning
A sequential circuit where state changes occur immediately in response to input changes, without a synchronizing clock signal.
- Term
Finite State Machine (FSM)
- Meaning
A mathematical model of computation used to design sequential logic. It consists of a finite number of states, transitions between states, and input/output actions.
Learning objectives
Understand the difference between combinational and sequential circuits.
Identify and analyze basic memory elements (latches and flip-flops).
Differentiate between synchronous and asynchronous sequential circuits.
Analyze state tables and state transition diagrams.
Understand the design process for simple sequential circuits like counters and registers.
Formulae
- Name
SR Flip-flop Excitation Table
- Note
X denotes 'don't care' or invalid state.
- Expression
S R | Q(t+1) --|---- 0 0 | Q(t) 0 1 | 0 1 0 | 1 1 1 | X (Invalid/Forbidden)
- Name
JK Flip-flop Excitation Table
- Note
Toggles the output if J=1, K=1.
- Expression
J K | Q(t+1) --|---- 0 0 | Q(t) 0 1 | 0 1 0 | 1 1 1 | Q'(t) (Toggle)
- Name
D Flip-flop Characteristic Equation
- Note
The output at the next clock edge is equal to the D input.
- Expression
Q(t+1) = D
- Name
T Flip-flop Characteristic Equation
- Note
Toggles output if T=1, holds if T=0.
- Expression
Q(t+1) = T ⊕ Q(t)
- Name
Mealy Machine Output Equation
- Note
Output depends on current state (Q) and current input (X).
- Expression
Y = f(Q, X)
- Name
Moore Machine Output Equation
- Note
Output depends only on the current state (Q).
- Expression
Y = f(Q)
Prerequisites
Combinational Circuits
Logic Gates
Boolean Algebra
Flip-flops (SR, JK, D, T)
State Transition Diagrams
Common mistakes
Confusing synchronous and asynchronous circuit behavior.
Incorrectly analyzing state transition diagrams.
Ignoring race conditions and hazards in asynchronous circuits.
Misunderstanding the clocking mechanism.
Practice preview
Which of the following is a characteristic of a sequential circuit?…
easy
What is the fundamental building block of most sequential circuits?…
easy
A JK flip-flop with J=1 and K=1 will:…
easy