A state table defines the overall behavior of a sequential circuit, a characteristic table describes the next-state behavior of a specific type of flip-flop, and an excitation table provides the necessary inputs to force a flip-flop into a desired next state .
Overview of sequential logic tables
| Feature | State Table | Characteristic Table | Excitation Table |
|---|---|---|---|
| Circuit Level | System or circuit level | Component (flip-flop) level | Component (flip-flop) level |
| Purpose | To analyze or design a sequential circuit's overall behavior. | To understand the fundamental operation of a specific flip-flop. | To design a sequential circuit using flip-flops. |
| Input Columns | Present state and external inputs. | Flip-flop inputs and present state (Qncap Q sub n 𝑄𝑛 ). | Present state (Qncap Q sub n 𝑄𝑛 ) and desired next state (Qn+1cap Q sub n plus 1 end-sub 𝑄𝑛+1 ). |
| Output Columns | Next state and external outputs. | Next state (Qn+1cap Q sub n plus 1 end-sub 𝑄𝑛+1 ). | Flip-flop inputs required to achieve the transition. |
| Direction | Predicts the future state and outputs based on current inputs and state. | Predicts the next state from the present state and inputs. | Determines the inputs needed to achieve a desired state transition. |
State table
A state table, also called a state transition table, is the primary tool for defining a finite-state machine (FSM) at the circuit level. It is analogous to a truth table for a combinational circuit but includes the present state as part of its inputs.
Structure
A state table is typically divided into four sections:
- Present State: The current state of the flip-flops, representing the circuit's memory.
- Inputs: The external inputs to the sequential circuit.
- Next State: The state that the flip-flops will transition to on the next clock edge.
- Outputs: The external outputs of the circuit, which may be a function of the present state and inputs.
Example: A simple sequential circuit
Consider a sequential circuit with one input (Xcap X
𝑋
) and one flip-flop with state Qcap Q
𝑄
.
| Present State (Qncap Q sub n 𝑄𝑛 ) | Input (Xcap X 𝑋 ) | Next State (Qn+1cap Q sub n plus 1 end-sub 𝑄𝑛+1 ) | Output (Ycap Y 𝑌 ) |
|---|---|---|---|
| 0 | 0 | 0 | 0 |
| 0 | 1 | 1 | 0 |
| 1 | 0 | 0 | 1 |
| 1 | 1 | 1 | 1 |
Role in analysis and design
- Analysis: If you have the circuit diagram, you can derive the state table to determine its full functionality.
- Design: Conversely, during design, a desired state table can be used to derive the necessary logic for the next-state and output sections of the circuit.
Characteristic table
A characteristic table describes the intrinsic behavior of a single type of flip-flop, such as a D, JK, or SR flip-flop. It is the most fundamental description of a flip-flop's operation.
Structure
The characteristic table defines the next state (Qn+1cap Q sub n plus 1 end-sub
𝑄𝑛+1
) as a function of the flip-flop's control inputs and its current state (Qncap Q sub n
𝑄𝑛
).
Example: JK flip-flop characteristic table
| J | K | Present State (Qncap Q sub n 𝑄𝑛 ) | Next State (Qn+1cap Q sub n plus 1 end-sub 𝑄𝑛+1 ) | Action |
|---|---|---|---|---|
| 0 | 0 | 0 | 0 | Hold |
| 0 | 0 | 1 | 1 | Hold |
| 0 | 1 | 0 | 0 | Reset |
| 0 | 1 | 1 | 0 | Reset |
| 1 | 0 | 0 | 1 | Set |
| 1 | 0 | 1 | 1 | Set |
| 1 | 1 | 0 | 1 | Toggle |
| 1 | 1 | 1 | 0 | Toggle |
Role in analysis
- In circuit analysis, the characteristic table is used to determine the next-state behavior of a circuit's individual flip-flops based on their inputs and current state. This is a building block for creating the circuit's overall state table.
Excitation table
An excitation table is a rearrangement of a flip-flop's characteristic table to facilitate the design of sequential circuits. Instead of showing the next state, it specifies the inputs required to cause a specific state transition.
Structure
The excitation table lists the present state (Qncap Q sub n
𝑄𝑛
) and the desired next state (Qn+1cap Q sub n plus 1 end-sub
𝑄𝑛+1
) as inputs. The outputs are the flip-flop's control inputs (e.g., J, K, D) needed to force that transition.
Example: JK flip-flop excitation table
| Present State (Qncap Q sub n 𝑄𝑛 ) | Next State (Qn+1cap Q sub n plus 1 end-sub 𝑄𝑛+1 ) | J | K |
|---|---|---|---|
| 0 | 0 | 0 | X |
| 0 | 1 | 1 | X |
| 1 | 0 | X | 1 |
| 1 | 1 | X | 0 |
| X denotes a "don't care" condition, meaning the input can be either 0 or 1. |
Role in design
- Design: During the design of a sequential circuit, you derive the overall state table first. Then, for each state transition in the state table, you use the flip-flop's excitation table to determine the necessary control inputs. These inputs can then be used to derive the Boolean equations for the flip-flop's input logic.