Flip-flops
Chapter4
Transformation between different flip-flops
Add the certain combinational logic
circuit to the input of the original flip-
flop
Original
flip-flop
Converting
circuit
Q’
Q
New flip-flop
New
excitation
input
Simultaneous
characteristic equation
Original
flip-flop
Converting
circuit
Q’
Q
converted flip-flop
X,Q Y
Yi=Fi(X,Q)
X be the input variable set of the new flip-flop
Y be the input variable set of the original flip-flop
Q be the present-state of the original flip-flop
Original
flip-flop
Converting
circuit
Q’
Q
converted flip-flop
X,Q Y
Convert JK to D,T,RS
JK >> D
J=f1(D,Q),K=f2(D,Q)
Qn+1=D=DQ’+D’Q
Qn+1=JQ’+K’Q
J=D,K=D’
JK >> T
J=f1(T,Q),K=f2(T,Q)
Qn+1=TQ’+T’Q
Qn+1=JQ’+K’Q
J=T,K=T
J
K
Q’
QC
D
J
K
Q’
QC
T
Convert JK to D,T,RS
JK >> RS
J=f1(R,S,Q),K=f2(R,S,Q)
Qn+1=S+R’Q (RS=0)
=S(Q’+Q)+R’Q
=SQ’+R’Q+SQ(R+R’)
=SQ’+R’Q+SR’Q
=SQ’+R’Q
J=S,K=Q
J
K
Q’
QCR
S
Convert D to JK,T,RS
D >> JK
D=f1(J,K,Q)
Qn+1=JQ’+K’Q
Qn+1=D
D=JQ’+K’Q
D >> RS
D=f1(R,S,Q)
Qn+1=S+R’Q
Qn+1=D
D=S+R’Q
D
Q’Q
C
K J
D
Q’Q
C
S R
Simultaneous excitation table
0
0
1
1
d
1
0
0
0
0
1
d
Qn+1 Qn R S J K T D
0
1
0
1
0
d
1
d
d
1
d
0
0
0
1
1
0
1
1
0
T >> RS
0
0
1
1
d
1
0
0
0
0
1
d
Qn+1 Qn R S J K T D
0
1
0
1
0
d
1
d
d
1
d
0
0
0
1
1
0
1
1
0
00 01 11 10
0
1
0
1
2
3
6
7
4
5
RSQ
1
1
d
d
T=SQ’+RQ
T =f(Q,R,S)
T >>D
0 1
0
1
0
1
2
3
DQ
1
1
T=DQ’+D’Q
T =f(Q,D)
0
0
1
1
d
1
0
0
0
0
1
d
Qn+1 Qn R S J K D T
0
1
0
1
0
d
1
d
d
1
d
0
0
0
1
1
0
1
1
0
JK>>RS
0
0
1
1
d
1
0
0
0
0
1
d
Qn+1 Qn R S J K T D
0
1
0
1
0
d
1
d
d
1
d
0
0
0
1
1
0
1
1
0
00 01 11 10
0
1
0
1
2
3
6
7
4
5
RSQ
d
1
d
d
d d
J=S
00 01 11 10
0
1
0
1
2
3
6
7
4
5
RSQ
d d dd
d 1
K=R
J =f(Q,R,S)
K =f(Q,R,S)
D >>JK
00 01 11 10
0
1
0
1
2
3
6
7
4
5
JKQ
11
1 1
D=JQ’+K’Q
D =f(Q,J,K)
0
0
1
1
d
1
0
0
0
0
1
d
Qn+1 Qn R S J K T D
0
1
0
1
0
d
1
d
d
1
d
0
0
0
1
1
0
1
1
0
Chapter4
Transformation between different flip-flops
Add the certain combinational logic
circuit to the input of the original flip-
flop
Original
flip-flop
Converting
circuit
Q’
Q
New flip-flop
New
excitation
input
Simultaneous
characteristic equation
Original
flip-flop
Converting
circuit
Q’
Q
converted flip-flop
X,Q Y
Yi=Fi(X,Q)
X be the input variable set of the new flip-flop
Y be the input variable set of the original flip-flop
Q be the present-state of the original flip-flop
Original
flip-flop
Converting
circuit
Q’
Q
converted flip-flop
X,Q Y
Convert JK to D,T,RS
JK >> D
J=f1(D,Q),K=f2(D,Q)
Qn+1=D=DQ’+D’Q
Qn+1=JQ’+K’Q
J=D,K=D’
JK >> T
J=f1(T,Q),K=f2(T,Q)
Qn+1=TQ’+T’Q
Qn+1=JQ’+K’Q
J=T,K=T
J
K
Q’
QC
D
J
K
Q’
QC
T
Convert JK to D,T,RS
JK >> RS
J=f1(R,S,Q),K=f2(R,S,Q)
Qn+1=S+R’Q (RS=0)
=S(Q’+Q)+R’Q
=SQ’+R’Q+SQ(R+R’)
=SQ’+R’Q+SR’Q
=SQ’+R’Q
J=S,K=Q
J
K
Q’
QCR
S
Convert D to JK,T,RS
D >> JK
D=f1(J,K,Q)
Qn+1=JQ’+K’Q
Qn+1=D
D=JQ’+K’Q
D >> RS
D=f1(R,S,Q)
Qn+1=S+R’Q
Qn+1=D
D=S+R’Q
D
Q’Q
C
K J
D
Q’Q
C
S R
Simultaneous excitation table
0
0
1
1
d
1
0
0
0
0
1
d
Qn+1 Qn R S J K T D
0
1
0
1
0
d
1
d
d
1
d
0
0
0
1
1
0
1
1
0
T >> RS
0
0
1
1
d
1
0
0
0
0
1
d
Qn+1 Qn R S J K T D
0
1
0
1
0
d
1
d
d
1
d
0
0
0
1
1
0
1
1
0
00 01 11 10
0
1
0
1
2
3
6
7
4
5
RSQ
1
1
d
d
T=SQ’+RQ
T =f(Q,R,S)
T >>D
0 1
0
1
0
1
2
3
DQ
1
1
T=DQ’+D’Q
T =f(Q,D)
0
0
1
1
d
1
0
0
0
0
1
d
Qn+1 Qn R S J K D T
0
1
0
1
0
d
1
d
d
1
d
0
0
0
1
1
0
1
1
0
JK>>RS
0
0
1
1
d
1
0
0
0
0
1
d
Qn+1 Qn R S J K T D
0
1
0
1
0
d
1
d
d
1
d
0
0
0
1
1
0
1
1
0
00 01 11 10
0
1
0
1
2
3
6
7
4
5
RSQ
d
1
d
d
d d
J=S
00 01 11 10
0
1
0
1
2
3
6
7
4
5
RSQ
d d dd
d 1
K=R
J =f(Q,R,S)
K =f(Q,R,S)
D >>JK
00 01 11 10
0
1
0
1
2
3
6
7
4
5
JKQ
11
1 1
D=JQ’+K’Q
D =f(Q,J,K)
0
0
1
1
d
1
0
0
0
0
1
d
Qn+1 Qn R S J K T D
0
1
0
1
0
d
1
d
d
1
d
0
0
0
1
1
0
1
1
0