Digital Logic Design

1. Digital Logic Design Lecture # 19 University of Tehran

2. Outline • Continuing on Designing a 110 Detector Using Moore Machine Method • Continuing on Designing a 011 Detector Using Mealy Machine Method

3. Continuing on Designing a 110 Detector Using Moore Machine Method • Let us continue the design of the sequence detector for 110, that we started last session. We saw the state diagram, now we want to work through a couple more states to be able to find the circuit itself. • First we change the state diagram to a tabular form as shown in this figure. This table is called a state table that nears the state diagram to tables we saw before, such as the KM etc.

4. Continuing on Designing a 110 Detector Using Moore Machine Method (continued…) • Ultimately we need a form of the above table that can be mapped in a KM. To do this we naturally need to replace the state names with numbers. We can use binary state assignment, where a unique binary number is used to represent each state. In order to make our state table more fitting to the KM we can use the state assignment shown in the previous slide.

5. Continuing on Designing a 110 Detector Using Moore Machine Method (continued…) • Redrawing the state table after state assignment we have the transition table as shown below: • Quote: Until now we haven’t ever talked about having a clock explicitly. But it can be implied from the fact that we have referred to a next state.

6. Continuing on Designing a 110 Detector Using Moore Machine Method (continued…) • The next step of our synthesis is a decision that has to be made about the type of flip flop we want to use. • Because of the 4 states we have we will need 2 feedback lines (referring to the Huffman model) and this means 2 flip flops with one clock on them. • The next stage (after choosing a particular flip flop) is to form an excitation table considering that particular flip flop in order to reach a stage where we can move what we’ve had so far to a KM.

7. Continuing on Designing a 110 Detector Using Moore Machine Method (continued…) • If we choose a D flip flop (as we will now for the last example), the excitation table will simply be a copy of the transition table we’ve seen above, this is because for a D flip flop we have Q+=D. Thus we have:

8. Continuing on Designing a 110 Detector Using Moore Machine Method (continued…) • Considering the Huffman model and the fact that we have now the excitation tables for the flip flop inputs we can find the glue logic needed before the inputs of the flip flops. This is done by mapping the data in the excitation table on a KM for D1 and D0:

9. Continuing on Designing a 110 Detector Using Moore Machine Method (continued…) • Quote: These maps can be filled by considering corresponding slices of the excitation table. • The KM for the outputs equation:

10. Continuing on Designing a 110 Detector Using Moore Machine Method (continued…) • Note: The outputs equation shows it’s independency of the input (as we are using Moore Machines). • With these equations we can now sketch the final logic circuit:

11. Continuing on Designing a 110 Detector Using Moore Machine Method (continued…) • The timing diagram of the above circuit looks something like the following figure: • We aren’t considered what the value of the output is between the clock pulses. Values are only important on the rising edges of the clock pulses (considering that we have used rising edge D flip flops).

12. Continuing on Designing a 110 Detector Using Moore Machine Method (continued…) • The mentioned method is valued because of its scalability and mechanical steps that makes it a good choice when it comes down to computer use for aid in design. • Note: Let’s consider a state where a hazard may occur in the point marked ‘*’ in the circuit of the last example. Reality has it that we needn’t worry about this happening because it can be easily solved by setting the clock frequency to work on the worst case delay and thus after any hazards that may occur in such parts of a circuit.

13. Continuing on Designing a 110 Detector Using Moore Machine Method (continued…) • Static flip flops can be used with any frequency less than the maximum which is decided considering the above mentioned, but when we are using dynamic flip flops we also need to be concerned about a minimum frequency, because data may be lost if we do not refresh the transistors in time.

14. Continuing on Designing a 011 Detector Using Mealy Machine Method • If we relax timing issues a little in our design, another sate machine that can be more minimal can be used. In this machine called the Mealy Machine, the output is dependent on input changes and thus is no longer synchronized to the clock. • The following is the Mealy machine for the 011 detector. The output changes to 1 as soon as the 0 of the sequence is seen.

15. Continuing on Designing a 011 Detector Using Mealy Machine Method (continued…) • Let’s follow the steps mentioned for turning the state diagram to the final circuit:

16. Continuing on Designing a 011 Detector Using Mealy Machine Method (continued…)

17. Continuing on Designing a 011 Detector Using Mealy Machine Method (continued…) • In some cases, relaxing time issues of the problem and using Mealy machines can help a lot in less hardware use. • The contribution of the input signal to the output in Mealy machines means less precision because any hazard on the input (noise, hazards from the levels before etc) can easily propagate onto the output. Because of such problems, Mealy machines can be never used in very precise designs.

18. Continuing on Designing a 011 Detector Using Mealy Machine Method (continued…) • The following timing diagram shows the differences in the two state machines output very clearly. The contribution of the input on the output can be seen in the timing diagram as well:

19. Continuing on Designing a 011 Detector Using Mealy Machine Method (continued…) • Quote: In synchronous sequential circuits we only care about the output’s value on clock pulses and we don’t care about its value at instances in between.