Latches,flipflops and counters - mbits-mirafra/digitalDesignCourse GitHub Wiki

The characteristic equation of flipflops and latches

Assuming clk or enable = 1 for all the states.

SR flipflop state diagram

Truth table

As per the truth table of SR flipflop, there are 4 possible input combinations namely 00, 01, 10, 11, and Q may be either 0 or 1. When SR = 00 and Q =0, the next state will be Q = 0 only. Similarly, when SR = 00 and Q = 1, the next state will be Q = 1 and it goes on according to the truth table.

The characteristic equation of SR flipflop

K map for Qn+1(next state)

For the group indicated by brown color Q varies so we do not consider it. And in SR, S is 1 and R is varying. Therefore the expression for this group is “S”.(since we have to consider the values which are not varying in the group). Another group at the corner has varying S and constant values of Q and S. therefore the value is QR’. Therefore the expression for Qn+1 can be given as

Qn+1 = S+QR’

JK flipflop state diagram

Truth table

Similar to SR there are four states in JK. if J and K both are and if Q is 0 then the next state will be 0 only. It implies that for the condition JK = 00, the state does not change. For JK = 01 and Q = 0, the next state will be 0 means the flipflop is in reset condition.

The characteristic equation of JK flipflop

K map for Qn+1(next state)

There are only 2 groups possible. In group 1(indicated by the brown color) K value is changing and the remaining are constants. So the expression for group 1 is JQ’. In the second group(indicated by the blue color) J value is changing and the remaining is constants. Therefore the second group becomes K’Q Combining both groups we get

Qn+1 = JQ’ + K’Q

D flipflop state diagram

Truth table

In D flipflop there are only 2 states either 0 or 1. The output follows the input.

The characteristic equation of D flipflop

K map for Qn+1(next state)

Qn+1 = D

T flipflop state diagram

Truth table

In T flipflop, if the input is 0 output does not change and if the input is 1, the output toggles i.e, if the present state is 0 next state will be 1, and vice versa.

The characteristic equation of T flipflop

Qn+1 = T’Q + TQ’ Since the above expression is similar to exor it can be rewritten as,

Qn+1 = T ⊕ Q

Note: The characteristic equation of flipflops and latches are similar.