JK to SR flip-flop conversion

To make a J-K flip-flop work as an S-R flip-flop, we find J and K as functions of S, R and the present state Q. The S-R behaviour: SR = 00 hold, 01 reset, 10 set, 11 not allowed (don't care).

Step 1: excitation table of the J-K flip-flop

Step 2: conversion table

Step 3: K-maps

K-map for J
Q\SR   00  01  11  10
 0      0   0   x   1
 1      x   x   x   x

K-map for K
Q\SR   00  01  11  10
 0      x   x   x   x
 1      0   1   x   0

• For J: the only 1 is at Q = 0, SR = 10. Grouping it with the don't-cares in column SR = 11 and in row Q = 1 gives $J = S$.
• For K: the only 1 is at Q = 1, SR = 01. Grouping with the don't-cares gives $K = R$.

$$J = S, \qquad K = R$$

Step 4: circuit

          +---------+
 S -------| J     Q |--- Q
 CLK -----|>  JK    |
 R -------| K    Q' |--- Q'
          +---------+

So S is connected straight to J and R straight to K. Check: SR = 10 gives JK = 10 (set), SR = 01 gives JK = 01 (reset), SR = 00 gives JK = 00 (hold), which is the S-R table.