SR Flip Flop

Truth table of SR latch

S* R* Q Q’
0 0 Not Used
0 1 1 0
1 0 0 1
1 1 Memory Element
• The output S* and R* can be written as
• S* = (S.Clk)’ = S’ + Clk’ and R* = (R.Clk)’ = R’ + Clk’
• When Clk = 0, S* = 1 , R* = 1, then SR FF acts like memory element.
• When Clk = 1, S*= S’ , R* = R’

• Function Table:
Clk S R Q Q’
0 X X Memory Element
1 0 0 Memory Element
1 0 1 0 1
1 1 0 1 0
1 1 1 Not Used
 Truth Table: Characteristic Table: Clk = 1
Q(t) S R Q(t+1)
Clk S R Q(t+1)
0 0 0 0
0 X X Q(t)
0 0 1 0
1 0 0 Q(t) 0 1 0 1
1 0 1 0 0 1 1 X
1 1 0 1 1 0 0 1
1 1 1 Invalid 1 0 1 0
1 1 0 1
Excitation Table: 1 1 1 X

Q(t) Q(t+1) S R K map for Q(t+1):

SR
0 0 0 X 00 01 11 10
Q(t)
0 1 1 0 0 0 0 X 1
1 0 0 1
1 0 X 1
1 1 X 0 1

Q(t+1) = S + Q(t) R’
 D Flip Flop
Characteristic Table:
Truth Table:
Q(t) D Q(t+1)
Clk D Q(t+1)
0 0 0
0 X Q(t)
0 1 1
1 0 0
1 0 0
1 1 1
1 1 1

Excitation Table: Q(t+1) = D

Q(t) Q(t+1) D
0 0 0
0 1 1
1 0 0
1 1 1
 JK Flip Flop
Truth Table:

Clk J K Q(t+1)
0 X X Memory; Q(t)
1 0 0 Memory; Q(t)
1 0 1 0
1 1 0 1
1 1 1 Toggle; Q(t)’

• The truth table for SR and JK flip flops are same for the first four combinations.
• In SRFF, S=1 and R=1, Q(t+1) is invalid
• Whereas in JK FF, J=1 and K =1, Q(t+1) = Q(t)’
Truth Table: Characteristic Table:
Clk J K Q(t+1) Q(t) J K Q(t+1)
0 X X Q(t) 0 0 0 0
1 0 0 Q(t) 0 0 1 0
1 0 1 0 0 1 0 1

1 1 0 1 0 1 1 1
1 0 0 1
1 1 1 Q(t)’
1 0 1 0
Excitation Table: 1 1 0 1
1 1 1 0

Q(t) Q(t+1) J K K map for J: K map for K:

0 0 0 X
Q(t+1) Q(t+1)
0 1 1 X
Q(t) 0 1 Q(t) 0 1
1 0 X 1 0 1 X X
0 0
1 1 X 0 1 X X 1 1 0

J = Q(t+1) K = Q(t+1)’
 K map for Q(t+1):
Clk J K Q(t+1) Q(t+1)’
JK 0 X X Q(t) Q(t)’
00 01 11 10
Q(t)
0 0 1 1 1 0 0 Q(t) Q(t)’
0
1 0 1 0 1
1 0 0 1
1
1 1 0 1 0
Q(t+1) = J.Q(t)’ + K’.Q(t) 1 1 1 ? ?

Race around Condition:

Condition to overcome Racing:

1) T/2 < propagation delay of FF.
2) Use edge triggering
3) Master – Slave operation is same as –ve edge triggering
 T Flip Flop
• T flip – flop is also known as “Toggle Flip – flop”.
• To avoid the occurrence of invalid state in SR flip – flop, one input is given to the flip – flop called
the Trigger input or Toggle input (T).
• Then the flip – flop acts as a Toggle switch. Toggling means ‘Changing the next state output to
complement of the present state output’.

Clk T Q(t+1)
0 X Q(t); Memory
1 0 Q(t); Memory
1 1 Q(t)’; Toggling
 Truth Table: Characteristic Table:

Clk T Q(t+1) Q(t) T Q(t+1)

0 X Q(t) 0 0 0
1 0 Q(t) 0 1 1
1 1 Q(t)’ 1 0 1
1 1 0

Excitation Table:

Q(t) Q(t+1) T Q(t+1) = Q(t) Ꚛ T

0 0 0
T = Q(t) Ꚛ Q(t+1)
0 1 1
1 0 1 Odd 1’s detector
1 1 0