 Hello everyone, I am Dr. Asha Thurangi and today we will be discussing finite state machines. These are the learning outcomes of this session. These are the contents we will be covering in this session. Now, before moving ahead pause this video and recall what are different types of digital circuits. Well, we all know that digital circuits are classified into two types combinational circuits which are memoryless circuits and sequential circuits which are circuits with memory or in other words circuits that make use of flip-flops and latches. Let us discuss combinational circuits. Combinational circuits are made up of basic logic gates that are combined or connected together to produce more complicated switching circuits. In this type of logic circuits output depends only on the current inputs and no memory elements are required. Figure shows the block diagram of combinational circuits. It consists of multiple inputs and one or more outputs. Also, output is expressed as a function of inputs. This figure shows the simple example of combinational circuit made up of logic gates having output Q. It is known as a logic diagram or a circuit diagram. This is one of the methods to represent combinational circuit. Truth table is a tabular representation method which specifies the output of the circuit for different input combinations. The same circuit can also be represented in the form of a logical or Boolean expression as shown where output is expressed as logical combination of inputs. This expression can be derived using KMAP method. Thus, the same logical circuit can be represented using various forms. Let us now see what is sequential circuit. Combinational circuits are combination of combinational circuits along with memory storage elements. They use flip-flops as memory elements and its output are known as state variables which together form the states. In this circuit, the output depends on the present values of the input signal as well as the sequence of past inputs. This figure shows the block diagram of sequential circuit. As shown, it consists of combinational circuit logic along with another block of memory elements. This figure shows an example of sequential circuit which is also known as logic schematic. As shown, the basic gates from the combinational circuit part and flip-flops make up the memory units. The functioning of the circuit is represented in the form of a state table instead of a truth table. From the given state table, with the help of excitation table of flip-flops, the state transition equations are derived. This is another form of representation of the sequential circuit where the next state and the outputs are represented in terms of functions of inputs and present state. State diagram is another graphical representation method of the sequential circuit which shows the functioning of the circuit along with different input and output values. Thus, it can be seen that the same sequential circuit can be represented in various different forms. Let us now see the state table and state diagram representation in detail. Another shows an example of a state table of a sequential circuit. State table as shown is a tabular representation of a functioning of a sequential circuit. The whole functioning of a circuit is expressed in three sections labeled as present state, next state and output. Present state reflects the state of flip-flops before the occurrence of a clock pulse. Present state reflects states of flip-flops after the clock pulse. The output section lists the value of the output variables for different input and present state values. Here, q1, q2 are known as state variables. If n is the total number of state variables for the circuit, then the circuit will have a total of m number of states where m is equal to 2 raised to n. Also, here x is input and z is output. Let us now discuss state diagram. Figure shows the state diagram for the state table we just discussed. As shown, it is the graphical representation of functioning of a sequential circuit. Here the state is represented by a circle and it is made up of state variables which are mentioned inside the circle. The state transition between the present states to the next state is indicated by the directed lines or arcs which are connecting the circles. Now along with this state transition line, the values of input and output which is associated with this state transition is specified in the format separated by the forward slash as shown. Thus, state diagram makes it easy to visualize the functioning of sequential circuit. Let us now discuss what is finite state machine? It is popularly known as FSM. Finite state machine is an abstract mathematical model of a sequential logic function. It has finite inputs, outputs and number of states. The basic idea of FSM is to store a sequence of different unique states and transition between them depending on the value of the inputs and the current states of the machine. They are implemented in real life circuits through the use of flip flops. Depending on how output is obtained, FSMs are classified into two types, Moore machine model and Millet machine model. Figure shows the block diagram of Millet machine model type of sequential circuit. As shown, the outputs of Millet machine depends on both the present state and inputs of the circuit that is output is a function of inputs and present state. Present state also depends on present state and inputs. On every clock cycle, combinational logic computes output and next state. Any changes in the input, it is reflected immediately in the change in the outputs. Thus, we can say that Millet machine has a synchronous output. Let us now discuss the state table and state machine representation for Millet machine. Figure shows the state table for Millet machine model. As shown, the present state section consists of all the states in which the circuit functions. Now depending upon the input value and the present state, the next state and the output is calculated and represented as shown. Thus, we can say that both output and next state depends upon the present state and input of the circuit. Figure shows the state diagram for the given state table. As shown, the 5 circles represent the 5 states of the circuit. Depending on the present state and the input, the state transition line points to the next state and the input and its respective output is specified on the state transition line. Figure shows the same state diagram, but in this 5 states A, B, C, D and E are encoded using 3 bit binary numbers. Also, using 3 bits, total of 8 combinations can be obtained out of which 5 are assigned to these 5 states. So, the remaining 3 combinations can be stated as unused states. It is up to the designer to specify what will be the next state if in case the system moves into one of these unused states. Most of the time in such situation, the next state will be the initial state or reset mode of the system. So, this is how the Mealy state machine is represented. Let us now discuss Moore machine model. Figure shows the block diagram for Moore machine model. Unlike Mealy machine, as shown in Moore machine, output depends only on the present state or current state of the circuit and not on the input values. And the next state depends both on present state and inputs similar to Mealy machine. Also, as output changes with state change, thus we can say that Moore machine has synchronous output. Let us now discuss the state table and state diagram representation of Moore machine. Figure shows the state transition table for Moore machine. As shown, the present state section consists of all states in which the circuit functions. Now, depending upon the input value and the present state, the next state is obtained and represented as shown. Here, the output section is mentioned separately. And the output value depends upon the present state of the circuit only. Figure shows the state diagram for the given state table using Moore model. Similar to Mealy machine, the five circles represents the five states of the circuit and depending upon the present state and input, state transition line points to the next state. Unlike Mealy machine, as shown in Moore machine representation, instead of specifying the output on the state transition line, here output is specified inside the state circle along with the present state as here output depends only on the present state. This is the major difference in representation of state diagram for Mealy and Moore machine model. Thus, in this section, we discussed types of digital circuits, FSM, Mealy and Moore machine models and its state table and state diagram representation. These are the references used, thank you.