# An Introduction to Finite State Machine Design

Roughly speaking, a synchronous Finite State Machine (FSM) refers to a digital circuit/system that has memory, and is driven by a clock signal to change from one state to another depending on the applied input and its previous state. This classification covers from the simplest circuit consisting of only one D flip-flop, to a high-performance computer system. One might refer to FSM as a sequential circuit, in contrast to a combinational circuit that is memoryless. With latest electronics/computer technology, an FSM of low to medium complexity can be designed and implemented rather easily using CPLD/FPGA and software tools. The main advantages of this approach are flexibility, compactness, and ease of maintenance. Hardwiring TTL/CMOS logic gate and DFF ICs together on a PCB is now considered outdated.

Previously on this website, we discussed some design and implementation of quadrature encoder interface circuits (see, for example, VHDL code for quadrature encoder receiver module and reference therein). That is an example of FSM which I normally use in my embedded system classes. I have found, however, that the circuit is somewhat too complicated to beginners who do not have enough background from a basic digital system course. So the purpose of this article is to provide a more simple example and hopefully help students grab the essence of two common approaches for FSM design: the State Diagram , and Algorithmic State Machine (ASM)
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# VHDL code for quadrature encoder receiver module

Original document: Quadrature Encoder Receiver Module : An Implementation on FPGA (.pdf)

In the original document cited above, we discussed some designs of quadrature encoder receiver module where Verilog code listings were included. This supplementary article provides the same implementations using VHDL. The development flows remain the same for both design A and B, so we basically list the codes and show simulation results here without repeating the design details.

### Design A

For Design A, the receiver module generates pulses at output pin U (up) or D (down), corresponding to whether A leads B, or A lags B, respectively (*). We showed the design process using STG (State Transition Graph) that yielded the results in equation (1) – (4) . The VHDL code for this implementation is in Listing 1 with simulation result shown in Figure 1. (The synthesis and behavioral simulation was performed using Xilinx Webpack 13.4 and Isim simulation, which could be downloaded from Xilinx website.

(*) It turns out that in the original document, the Karnaugh map for output U and D shuffles, so as the resulting equations (3) and (4). You could verify from the simulation in Figure 9. If this gives the wrong sense for your motor setup, simply switch equation (3) and (4). We do so in the VHDL code below.

# A bit of history on why this site ends up here.

Dear Readers of scilab.ninja and dew.ninja

In case you wonder why these two sites are moved (and controlsystemslab.com and mushindynamics.com are gone). Here is my explanation.