 Hello everyone welcome to this session of flip-flop analysis. In today's session we are going to analyze T flip-flop. So, at the end of this session you will be able to derive the characteristic equation from the characteristic table of toggle flip-flop. You will be also able to discuss the state table and state diagram of T flip-flop derive the excitation table for toggle flip-flop. So, this analysis of flip-flop will help you whenever you go into design flip-flop based applications like counter designs, finite state machine designs etcetera. So, let us first revisit the characteristic table of toggle flip-flop. So, you can derive the characteristic table from the function table of T flip-flop. So, this table specifies the functional behavior of your flip-flop. So, input column consists of clock and T whereas output column consists of the next state and the complement of the next state. So, the characteristic table you can derive from this function table which lists the next state for each combination of T inputs and the present state. So, here the function table shows you that when T is equal to 0 next state is always same as the present state, but when T is equal to 1 the next state is always complement of the present state. So, you can call this as a no change and complement respectively. Now, let us use this function table to derive the characteristic table. So, to derive the characteristic equation you require the characteristic table. So, this is the characteristic table of your T flip-flop. So, when T is equal to 0 and present state is 0 the next state is 0, when T is equal to 0 present state is 1 next state is 1. So, these two rows tells you that when T is equal to 0 the next state is having no change. Next state preserve the present state or next state is equal to present state. Third row when T is equal to 1 and present state is 0 next state is 1. When T is equal to 1 present state is 1 next state is 0. So, last two rows specifies the relation between next state and present state and the relation is complement. So, you can derive this table from the function table. Now, let us derive the characteristic equation using this table. So, we are just going to derive the expression for next state that is QT plus 1. So, we will require here a two variable K map and the inputs we are using for this two variable K map are T and Q. So, T is used for column whereas QT that is present state is used for rows addressing rows. Now, by mapping this next state column on this K map you will see that you have two main terms, minterm 1 and minterm 2, but there is no grouping possible that is why we will keep these two groups as a single groups and we will go for the final expression. So, the first group is minterm 2 I have written in the expression the product term for this group is T Q bar for the second group second single group the product term is T bar Q. So, I will add this add these two product terms and I have written here the next state expression in SOB form that is T Q bar plus T bar Q. So, this is nothing but the characteristic expression or equation for T flip flop. So, this is unique and this expression you will be required whenever you are designing different applications based on the T flip flop. For example, counters and state machines. Now, let us go to the next point that is state table of T flip flop. So, let us understand what is a state table. State table shows you the transition of flip flop from present state to the next state for various input combinations. So, with the present state and the flip flop input the next state of the flip flop can be determined by the characteristic table. So, the meaning is that you can derive the state table from the characteristic table. Let us see how. So, please take some time and write the characteristic table of T flip flop. So, here on the left hand side you will see that the characteristic table of T flip flop is drawn whereas, on the right hand side we have derived the state table for the T flip flop. So, let us understand how we have derived this state table. So, the input column of the state table is the present state whereas, the output column of the state table is nothing but the next state values for different input combinations. So, let us consider this first row of characteristic table where T is 0, present state is 0 and next state is 0. So, let us understand how we have written the state table from the characteristic table. So, here the present state is 0, when T is equal to 0 what is the next state? So, next state is 0. So, this is the case you will see on the state table present state 0, T is 0, the next state is 0. Similarly, present state is 1, T is 0, the next state is 1, then present state 0, T is 1, next state is 1 and the last case present state is 1, T is 1, the next state is 0. So, this is how you can actually derive the state table for your flip flop with the help of characteristic table. Let us go to the next point that is state diagram. So, you can derive the state diagram with the help of state table. Let us see how a state diagram is a graph with nodes and directed edges. So, these edges are used for connecting different nodes. So, nodes are here labeled with the state of the flip flop. So, T flip flops comes with two states 0 and 1 that is why here two circles are drawn or you can say that two nodes are drawn and these two nodes are labeled with the state value that is 0 and 1. The directed edges are labeled with the flip flop inputs. So, these are the directed edges and you will see that these are named with the flip flop inputs. So, these inputs actually causes the transition from one state to another state. So, let us see how this state diagram can be derived from the state table. So, let us consider this first case when present state is 0 and T is 0. So, here you will see that present state is 0 and T is 0 the next state is remain 0 ok. Next case present state 0 T is 1 next state changes to 1 ok. So, the present state is 0 T is 1 the next state is 1. So, here the transition happened then present state is 1 T is 0 next state is same. So, this is the case present state 1 T is 0 next state will remain 1 and the last case present state 1 T is 1 the next state is 0. So, the state diagrams helps you to draw the state diagrams for the different applications like counters and finite state machines based on the flip flops. Now, let us go to the next point that is excitation table. So, let us understand what is the excitation table. Excitation table provides the excitations required to change a flip flop from one state to another state that is desired state. So, flip flop input T is represented as a dependent function of state transition. So, you will see here the excitation table the input columns are the present state and next state whereas, the output column is T that is flip flop input. So, let us understand how we are going to derive this excitation table from the state diagram. So, let us consider the state 0 present state 0. If you want next state 0 the value of T input should be 0. So, this is the first row present state 0 next state 0 you required to apply T is equal to 0. Let us go to the next case present state 0 if you want next state 1 apply T is equal to 1. So, this is the second row present state 0 next state 1 apply T is equal to 1. Third row present state 1 if you want next state as a 0 apply T is equal to 1 ok. So, this is the third row present state 1 if you want next state 0 apply T is equal to 1. The last combination last row present state 1 next state if you want 1 then apply T is equal to 0. So, present state 1 next state 1 apply T is equal to 0. So, this is how you can actually derive the excitation table for the T flip flop using state diagram of T flip flop. A particular state transition predicts the flip flop inputs required for the state change desired state change. So, the excitation tables are used in the design and synthesis of synchronous sequential machines. These are the references you can go for further reading. Thank you.