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cpe229_lec03

# cpe229_lec03 - CPE 229 Course Notes Lecture 3 Copyright...

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CPE 229 Course Notes: Lecture 3 Copyright: 2005 Bryan Mealy The Real FSM Story Up until now, we have taken two approaches to learning the ins and outs (pun intended) of finite state machines: analysis and design. The approach we took in these types of problems was well-structured which hopefully helped to offer some insights into the workings of the FSM. As you probably also may have noticed, the approach was somewhat tedious. The only saving grace for this approach to FSM problems was the fact that the problems were not too complex. The key word in the previous sentence is “complex”. The characteristic that made the approach complex was the fact that all of the inputs to the Next State Decoder (see Figure 1) necessarily appeared as independent variables in the resulting truth table. Figure 1 shows a block diagram of a FSM (Moore-type). So long as the inputs to the Next State Decoder block remained relatively few, the resulting truth table remained relatively small the problems remained relatively doable. The problem is that complex problems were not doable with this approach (and even the simple ones took too long to do). The approach we’ve used to design FSMs is referred to as the classical approach. Although it is instructive and interesting (and tedious), we need to come up with other techniques to allow us to work with more complex problems. This set of notes provides the background and example of the “new” FSM techniques that allow us to move past the grunt limitations presented by the classical FSM approach (truth table and K- map-based). The first part of this set of notes provides an example that shows the motivation behind the new approaches. The second example shows an actual application of the techniques. Figure 1: A block diagram for a FSM (Moore-machine). Motivation for the New FSM Techniques Consider the simple counter design shown in Figure 2(a). The associated PS/NS table is shown in Figure 2 (b). MOST IMPORTANT FACT: We’ll be mostly interested in the Y1 Y1 + transition in this motivational example. This is because the Y1 state variable represents every possible transition for a single storage element: (0 0, 0 1, 1 1, and 1 0). The Y2 variable is shown in the following text but it is less instructive because not all the possible state transitions are represented. Y1 Y2 Y1 + Y2 + 0 0 0 1 0 1 1 0 1 0 1 1 1 1 0 0 (a) (b) Figure 2: State diagram and PS/NS table for simple counter. 1

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CPE 229 Lecture 3 Notes For this example, we’ll be generating the excitation inputs for D, T, and JK flip-flops. In other words, we want to implement this counter using two D’s, then two T’s, then two JK flip-flops. Figure 3 shows the excitation data for the D1 and D2 flip-flops. Note that the D1 and D2 columns match the corresponding next-state variables which is necessarily true for D flip-flops 1 . From this point, using the classical FSM approach, you would then drop the D1 and D2 excitation data into a K-map and generate the
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