Present State
(PS/NS)
Yi Yi+
Ji Ki
Comment
User for 1s
(Set-Hold 1)
Use for 0s
(Clear-Hold 0)
0 0
0 1
1 0
1 1
0 -
1 -
- 1
- 0
Hold 0 transition
Set transition
Clear transition
Hold 1 transition
Ji
Ki
Ji’
Ki’
**Note: “-“ indicates don’t care
The “Set – Clear Method” can be used to obtain the J-K excitation equations for the 1s of
each state variable (flip-lop outputs)
Ji = ∑ (PS .external input conditions for set) when Yi = 0 for i=1,2,3,...
Ki = ∑ (PS .external input conditions for clear) when Yi = 1 for i=1,2,3,...
Note: This method solves for 1’s of the function.
We could also apply the “Hold 0 - Hold 1 Method” to obtain the T excitation equations for the
0s of each state variable (flip-flop outputs)
Ji’ = ∑ (PS .external input conditions for hold 0) when Yi = 0 for i=1,2,3,...
Ki’ = ∑ (PS .external input conditions for hold 1) when Yi = 1 for i=1,2,3,...
Note: This method solves for 0’s of the function and it is equivalent to first method.
Example - J-K excitation Equation from state diagram
Design a synchronous 2-bit Binary up down counter that counts up when input signal X=0 and
counts down when input signal X=1
State Y1Y2
Input X
Use the “Set – Clear Method” to obtain the J-K excitation equations for the 1s of each state
variable (flip-flop outputs)
- By observing all the sets (Y1 =0 Y1 +=1), we can write the J1 excitation equation, from
the state diagram:
J1 = Y1’.Y2.X’ + Y1’.Y2’.X = Y2’.X + Y2.X’ - By observing all the clears (Y1 =1 Y1+=0), we can write the K1 excitation equation,
from the state diagram:
K1 = Y1.Y2’.X + Y1.Y2.X’ = Y2’.X + Y2.X’
Repeat Step 1 for the second Flip Flop
Use the “Set – Clear Method” to obtain the J-K excitation equations for the 1s of each state
variable (flip flop outputs)
- By observing all the sets (Y2 =0 Y2 +=1), we can write the J2 excitation equation, from
the state diagram:
a
00
b
01
c
10
d
11