Various Representation of Flip-Flops

Various Representation of Flip-Flops

AU May-04,05,06,07,08,09,10,11,15, Dec.-03,07,09,10, June-16

Characteristic Equations of Flip-Flops

• The characteristics equations for various flip-flops are summarized in Table 2.5.1.

Flip-Flops as Finite State Machines

• Fig. 2.5.1 shows the state transition diagram for all flip-flops. Here, the 0 and the 1 in the circle represents the two states of the flip-flops and the arcs with arrow heads indicate the state transitions for specific inputs of the flip-flop.

• For example, when SR flip-flop is in state 0, it goes to state 1 if SR inputs are 10, i.e. S = 1 and R = 0.

Flip-Flop Excitation Table

• A truth table that lists the required inputs conditions for a given change of state. Such a table is known as an excitation table of the flip-flop.

SR Flip-Flop

• Table 2.5.2 (a) and (b)show the truth table and excitation tables for SR flip-flop, respectively.

• There are four possible transitions from the present state to the next state.

• For each transition, the required input condition is derived from the information available in the truth table.

Note The symbol "X" in the table represents a don't care condition, i.e., it indicates

that to get required output it does not matter whether the input is either 1 or 0.

• 0 → 0 Transition: The present state of the flip-flop is 0 and is to remain 0 when a clock pulse is applied. Looking at truth table of SR flip-flop we can understand that, this can happen either when R = S = 0 (no-change condition) or when R = 1 and S = 0. Thus, S has to be at 0, but R can be at either level. The table indicates this with a "0" under S and an "X" (don't care) under R.

• 0 → 1 Transition: The present state is 0 and is to change to 1. This can happen only when S = 1 and R = 0 (set condition). Therefore, S has to be 1 and R has to be 0 for this transition to occur.

• 1→ 0 Transition: The present state is 1 and is to change to a 0. This can happen only when S = 0 and R = 1 (reset condition). Therefore, S has to be 0 and R has to be 1 for this transition to occur.

• 1 → 1 Transition: The present state is 1 and is to remain 1. This can happen either when S = 1 and R = 0 (set condition) or when S = 0 and R = 0 (no change condition). Thus R has to be 0, but S can be at either level. The table indicates this with a "X" under S and "0" under R.

JK Flip-Flop

• The truth table and excitation table for JK flip-flop are shown in Table 2.5.3 (a) and (b) respectively.

• 0→0 Transition: When both present state and next state are 0, the J input must remain at and the K input can be either 0 and 1.

• 0 → 1 Transition: The present state is 0 and is to change to 1. This can happen either when J = 1 and K = 0 (set condition) or when J = K = 1 (toggle condition). Thus, J has to be 1, but K can be at either level for this transition to occur.

• 1→0 Transition: The present state is 1 and is to change to 0. This can happen either when J = 0 and K = 1 or when J = K = 1. Thus, K has to be 1 but J can be at either level.

• 1→ 1 Transition: When both present state and next are 1, the K input must remain at 0 while the J input can be 0 or 1.

• The excitation table for JK flip-flop has more don't care conditions than the excitation table for RS flip-flop.

• The don't care terms usually simplify the function. Therefore, the combinational circuits using JK flip-flops for the input functions are likely to be simpler than those using RS flip-flops.

D Flip-Flop

• The Table 2.5.4 (a) and (b) show the truth table and excitation table for

D flip-flop, respectively.

• In D flip-flop, the next state is always equal to the D input and it is independent of the present state. Therefore, D must be 0 if Q_n+1 has to be 0, and 1 if Q_n+1 has to be 1, regardless of the value of Q_n.

T Flip-Flop

• The Table 2.5.5 (a) and (b) show the truth table and the excitation table for T flip-flop, respectively.

• When input T = 1, the state of the flip-flop is complemented; when T = 0, the state of the flip-flop remains unchanged. Therefore, for 0 → 0 and 1 → 1 transitions T must be 0 and for 0 → 1 and 1 → 0 transitions T must be 1.

Example 2.5.1 Show that the characteristic equation of Qʹ_(t+1) of JK flip-flop is Qʹ_(t+1)= J'Q' + KQ  AU Dec.-07, Marks 4

Solution: From Fig. 2.5.2 we can write truth table for JK flip flop as shown below.

Example 2.5.2 Explain the difference between a state table, characteristics table and an excitation table.  AU: May-15, Marks 6

Solution :

Review Questions

1. Give the characteristic equation and state diagram of JK flip-flop.  AU: May-04, 10, 11, Dec.-09, Marks 2

2. Give the excitation table for JK flip-flop.  AU: May-05, 06, 09, Dec.-10, June-16 Marks 2

3. Obtain the excitation table of D flip-flop.  AU May-06, Dec.-10, Mark 1

4. Give the state diagram of JK flip-flop.  AU May-07, Marks 2

5. What is excitation table?  AU May-08, Marks 2

6. Give state diagram of JK flip-flop.  AU May-10, Marks 2

7. Draw state diagram of SR flip-flop.  AU: Dec.-10, Marks 2

8. Draw the truth table and excitation table of T flip-flop.  AU: Dec.-10, Marks 2

9. State the characteristics equations of various flip-flops.