PowerPoint PresentationSlide 2Slide 3Slide 4Slide 5Slide 6Slide 7Slide 8Slide 9Slide 10Slide 11Slide 12Slide 13Slide 14Slide 15Slide 161Synchronous Logic Circuits versus Combinational Logic CircuitsLet’s begin by comparing how we describe each type of circuit.Descriptions of Combinational Logic CircuitsRecall that there are numerous ways to describe a combinational logic circuit, including:•truth tables•Karnaugh maps(minterms)(maxterms)•Boolean expressions•SOP expressions•POS expressions•Logic diagrams•VHDL descriptionsNote: Given any one of the descriptions above, we could determine all of the others.Reading Assignment: - Chapter 5 in Logic and Computer Design Fundamentals, 4th Edition by Mano- Online supplement to text “Design and Analysis using JK and T Flip-Flops”(www.prenhall.com/mano)Lecture #12 EGR 270 – Fundamentals of Computer Engineering2Descriptions of Sequential Logic CircuitsSimilarly, there are numerous ways to describe a sequential logic circuit, including:•State diagrams•State tables•State equations and output equations•Input equations (flip-flop input functions) and output Equations•Logic diagrams•VHDL descriptionsNote: Given any one of the descriptions above, we could determine all of the others.Some of these ways to describe sequential circuits will now be introduced.Lecture #12 EGR 270 – Fundamentals of Computer EngineeringFinite State Machines (FSM) – Sequential circuits are also referred to as finite state machines. The circuit operates by moving between a finite number of pre-determined states.3State DiagramsThis is the most common way to describe a sequential circuit.A state diagram is somewhat like a flowchart that describes the sequence to states through which the circuit might progress.State – a distinct event that is to occur (one event in a sequence)Example: A state might be a single count in a counter. If a counter counts 0, 1, 2, ….. , 9 and then repeats, then it has 10 unique states. If four flip-flops were used to store the count, then the flip-flops would store the values 1001 corresponding to state 9.Example: A state might be one step in a machining operation (there might be 5 states corresponding to the operations drill, ream, counterbore, countersink, and polish).Example: A traffic light controller might have three states: Green, Yellow, and Red. Under certain input conditions or at certain times, the controller will change state. Lecture #12 EGR 270 – Fundamentals of Computer Engineering4Encoding states – Show how a binary code can be stored in a set of flip-flops.In most cases, Number of flip-flops needed = log2(Number of states)Example: Determine the number of states needed in each case below:Description of circuit Number of flip-flops requiredCircuit with 20 statesTraffic light controller3-bit UP/DOWN counterDecade counterLecture #12 EGR 270 – Fundamentals of Computer Engineering5There are two primary types of state diagrams (state machines):Mealy state machine (Mealy model) – the output depends on the present state and the inputs applied.Moore state machine (Moore model) – the output only depends on the present state. A B X/Y Mealy Model •Transition from one state to another depends on the Input, X•Output, Y, is specified with the transition•Output, Y, depends on both the Present State and the Input, X A/Y B/Y X Lecture #12 EGR 270 – Fundamentals of Computer Engineering CX/YMoore Model•Transition from one state to another depends on the Input, X•Output, Y, is specified with the Present State•Output, Y, depends only on the Present StateX C/YWe will primarily use Mealy models6Example: Both a Mealy Model and a Moore Model are used below to specify state machines that will detect the occurrence of two 1’s in a row.Lecture #12 EGR 270 – Fundamentals of Computer Engineering•Two states (one flip-flop)•Output of 1 indicates that two inputs of 1 occurred in a row.•Output is not associated with a state, but with the transition.•Three states (two flip-flops)•Output of 1 indicates that two inputs of 1 occurred in a row.•Output is associated with state C.State A: Zero 1’s receivedState B: One 1 receivedState A: Zero 1’s receivedState B: One 1 receivedState C: Two 1’s receivedAB1/00/01/10/0A/0B/0100C/1101Mealy Model:Moore Model:7Comparison of Mealy models and Moore models:Lecture #12 EGR 270 – Fundamentals of Computer EngineeringMealy Model Moore ModelOutput depends on both the Present State and the InputsOutput depends only on the Present StateSpecify output in transition Specify output in Present StateGenerally requires fewer states Generally requires more statesOutput may change immediately when input changes, so may change in the same clock cycleOutput does not respond immediately to input change, but is synchronized with the clockReacts faster to inputs SaferMost of our textbook examples and class examples will use Mealy models8Examples of state diagrams:A) Modulo-5 (mod-5) counter:B) 3-bit Up/Down counter:C) Traffic Light ControllerLecture #12 EGR 270 – Fundamentals of Computer Engineering9State Table A state table provides the same information as the state diagram, but in tabular form.Example: Determine the state table for the state diagram shown below. B C A D 0/0 1/1 1/0 1/0 1/0 0/0 0/1 0/1 Lecture #12 EGR 270 – Fundamentals of Computer EngineeringIs this a Mealy machine or a Moore machine?10State Assignment Some state diagrams have states indicated by letters or names because there is no numeric value assigned to the states. As an example, there are no natural numeric values for the states in a circuit that controls a traffic light (states, RED, YELLOW, and GREEN). In such cases, numeric values must be assigned to each state. In the case of the traffic light, 2 bits are needed to encode the three states, but various possible codes could be used. For example, RED = 00, YELLOW = 01, and GREEN = 10. There are many other possible state assignments. Which is the best assignment to use? We don’t know. This is a current research topic.Example: List possible state assignments for the last problem and repeat the state table using one of the state assignments.Lecture #12 EGR 270 – Fundamentals of Computer Engineering11Determining the State Diagram from a Logic DiagramThe state diagram or state table can be found from the logic diagram by assuming an