Step 2) Determine the number of flip-flop based on the number of states
(#states = 3) ≤ 2 (#flip-flop = 2) assuming full encoding.
Step 3) Assign Unique code to each state
a: 00, b:01; C:11
Step 4) Write the excitation-input equations
The JK flip-flop excitation equation is JK Y+ = J.Y’ + K’.Y
You may derive the general excitation equation from the characteristic table for the JK
flip-flop to obtain the excitation table for the JK flip-flop, as shown below:
Write the PS/NS table for JK, flip-flops (this intermediate step is helpful)
Draw the Composite K-map for each of the desired outputs Y1+ ,Y2 +, Z:
00
01
11
10
Y1Y2 J1 K1 J2 K2 Z
0 1 1
1 0 1
0 1 0
- - -
0 1
0 1
1 0
- -
J 1 = Y1’.Y2
K 1 = Y1 + Y2’
J 2 = Y1’
K 2 = Y1
Z = Y1’
Note: “-“ means don’t care
Y 1 Y 2 Y 1 + Y 2 + J 1 K 1 J 2 K 2 Z
0 0 0 1 0 1 1 0 0
0 1 1 1 1 0 1 0 1
1 1 0 0 0 1 0 1 1
1 0 - - - - - - -
Unused State
J K Y Y +^
0 0 0 0
0 0 1 1
0 1 0 0
0 1 1 0
1 0 0 1
1 0 1 1
1 1 0 1
1 1 1 0
Characteristic
table Output Excitation
table
Y Y+ J K^
0 0 0 -
0 1 1 -
1 0 - 1
1 1 - 0
Input Excitation
table
Note: “-“ = don’t care
J = Y +^
K = Y +’
Input-Excitation Eq.