SR to T conversion and SR timing diagram

Converting S-R flip-flop to T flip-flop

A T flip-flop must hold for T = 0 and toggle for T = 1. We generate S and R from T and Q.

S-R excitation table:

Conversion table (Q+ = T XOR Q, then S and R from the excitation table):

K-maps:

K-map for S
Q\T    0   1
 0     0   1
 1     x   0

K-map for R
Q\T    0   1
 0     x   0
 1     0   1

$$S = T\,\overline{Q}, \qquad R = T\,Q$$

            +-----+      +---------+
 T --+----->|     |      |         |
     | Q' ->| AND |----->| S     Q |---> Q
     |      +-----+      |         |
     |      +-----+ CLK->|>  SR    |
     +----->|     |      |         |
       Q -->| AND |----->| R    Q' |---> Q'
            +-----+      +---------+
 (Q and Q' are fed back from the outputs)

Check: T = 1, Q = 0 gives S = 1, R = 0 (Q goes to 1); T = 1, Q = 1 gives S = 0, R = 1 (Q goes to 0); T = 0 gives S = R = 0 (hold). S and R are never 1 together.

Timing diagram of S-R flip-flop (positive edge triggered, Q initially 0)

       1   2   3   4   5   6
CLK   _|‾|_|‾|_|‾|_|‾|_|‾|_|‾|
S     ‾‾‾|___________|‾‾‾|____
R     _______|‾‾‾|_______|‾‾‾|
Q     _|‾‾‾‾‾‾‾|_______|‾‾‾|__

S = 1 sets Q at an edge, R = 1 resets it, S = R = 0 keeps the old value. S = R = 1 is not applied because it is invalid.