Using RS Flip Flop to Realize D flip-flop


In the previous articles we discussed about the various types of flip-flops that are being used in various storage elements, and also talked about master slave flip flops. But there is a necessity for us to convert one type of flip-flop into another. For example, consider we have a JK flip-flop. But we need a D flip-flop to successfully implement a storage element. In this case instead of forming a new flip-flop, we can directly convert the JK flip-flop into a D flip-flop. This process is called as Realization of Flip-flop.

In this article let us discuss about converting a RS Flip flop into a D flip-flop.

Excitation and Truth Table: RS flip flop

Before elaborating the realization process, let us briefly discuss the Excitation table and Truth Table of RS flip flop.

RS Truth Table

From the above truth table we can deduce that:

Regardless of the value of R input, when the S input is 0 the value of present state Q is retained. Consider the first 2 rows of the above table.

RS Table1

Similarly consider the 5th row and 7th row of the RS truth table.

RS Table 2

Regardless of the value of S, When R is 0, the present state Q is retained for the next state Q (t+1).

From the above conclusions we can form the excitation table of RS flip-flop as shown below.

RS excitation table

In the above Figure, X represents don’t care condition (value has no significance). For example if X is found under R input, it indicates that the value of R will not affect the present or future (or) next state of the flip-flop.

From the above discussions we can conclude that, there are four possible transitions for a RS flip-flop.

The four transitions are:

0->0 transition; 0->1 transition, 1-> 0 transitions and 1 -> 1 transition.

Exciataion and Truth Table: D Flip-Flop

Now let us discuss the Truth table and excitation table of D Flip-Flop.

D truth table
D Flip-Flop excitation table

From the above table it is clear that for a D flip-flop, the next state Q (t+1) is always equal to the D input. The next state Q (t+1) is independent of the present state Q.

From the K-map and excitation table we can say that the characteristic equation of D flip-flop is

Q (t+1) =D

K-map D flip-flop

Converting an RS flip-flop To D Flip-flop

We can convert one flip-flop to another flip-flop by adding some additional gates to the existing flip-flop or giving some extra connections.

To convert a RS flip-flop into D flip-flop, we simply have to remap the state transitions of D flip-flop’s K-map into equations of R and S inputs of flip-flop.

RS to D Exciatation Table

The procedure for conversion of RS flip-flop to D flip-flop is as follows.

· Draw the K-map of R and S inputs separately with Input D and Present state Q.

· Fill the K-map using the data in the excitation table. When D=0 and Q=0, the next state Q (t+1) is 0. (Refer to D flip-flop truth table). For the next state to remain 0, the value of R and S should be X and 0 respectively. Here X denotes don’t care value. The value of R in this condition, will not affect the state of the system. 0->0 transition. R=X and S=0.

· When D=0 and Q=1, the value of Next state Q (t+1) should be 0. (Refer to D flip-flop truth table). Here there is a transition from 0 to 1. [Q=1 and Q (t+1) =0]. The RS input which corresponds to this transition is S=0 and R=1. 1-> 0 transition, R=1 and S=0.

· When D=1 and Q=0, the value of next state Q (t+1) should be 1(from D flip-flop truth table). Here there is 0 to 1 transition. The value of R and S should be 0 and 1 respectively. 0->1 transition, R=0 and S=1.

· When D=1 and Q=1, the value of next state should be equal to 1(from D flip-flop truth table). Here there is a 1->1 transition. The value of R and S corresponding to this transition is 0 and X respectively. X here represents don’t care condition. 1->1 transition, R=0 and S=X.

Thus from the above steps it is clear that the RS flip-flop can be converted to a D flip-flop.

K-Map and Logic diagram gives us a better understanding about the conversion of RS flip-flop to D flip-flop.

From the K-Map, we can conclude that S=D and R=D’.

K-map for S Input

K-map for R Input

Logic Diagram

From the Logic diagram we can conclude that, S=D. D input is directly given to S input of RS flip-flop and Instead of R input, the complement of D value is given to R input.

Thus we can convert a RS flip-flop into a D flip-flop.

Logic Diagram RS-D flipflop

In the Next article let’s discuss the other types of flip-flop conversions.