A flip-flop is a sequential digital electronic circuit having two stable states that can be used to store one bit of binary data. Flip-flops are the fundamental building blocks of all memory devices.

Types of Flip-Flops

S-R Flip-Flop
J-K Flip-Flop
D Flip-Flop
T Flip-Flop

S-R Flip-Flop

This is the simplest flip-flop circuit. It has a set input (S) and a reset input (R). When in this circuit when S is set as active, the output Q would be high and the Q' will be low. If R is set to active then the output Q is low and the Q' is high. Once the outputs are established, the results of the circuit are maintained until S or R get changed, or the power is turned off.

Truth Table of S-R Flip-Flop

S	R	Q	State
0	0	0	No Change
0	1	0	Reset
1	0	1	Set
1	1	X

Characteristics Table of S-R Flip-Flop

S	R	Q(t)	Q(t+1)
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	X
1	1	1	X

Characteristics Equation of S-R Flip-Flop

$$\mathrm{Q(t \: + \: 1) \: = \: S \: + \: R' \: Q(t)}$$

J-K Flip-Flop

Because of the invalid state corresponding to S=R=1 in the SR flip-flop, there is a need of another flip-flop. The JK flip-flop operates with only positive or negative clock transitions. The operation of the JK flip-flop is similar to the SR flip-flop. When the input J and K are different then the output Q takes the value of J at the next clock edge.

When J and K both are low then NO change occurs at the output. If both J and K are high, then at the clock edge, the output will toggle from one state to the other.

Truth Table of JK Flip-Flop

J	K	Q	State
0	0	0	No Change
0	1	0	Reset
1	0	1	Set
1	1	Toggles	Toggle

Characteristics Table of JK Flip-Flop

J	K	Q(t)	Q(t+1)
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

Characteristics Equation of JK Flip-Flop

$$\mathrm{Q(t \: + \: 1) \: = \: j \: k \: Q(t)' \: + \: K'Q(t)}$$

D Flip-Flop

In a D flip-flop, the output can only be changed at positive or negative clock transitions, and when the inputs changed at other times, the output will remain unaffected. The D flip-flops are generally used for shift-registers and counters. The change in output state of D flip-flop depends upon the active transition of clock. The output (Q) is same as input and changes only at active transition of clock

Truth Table of D Flip-Flop

D	Q
0	0
1	1

Characteristics Equation of D Flip-Flops

$$\mathrm{Q(t \: + \: 1) \: = \: D}$$

T Flip-Flop

A T flip-flop (Toggle Flip-flop) is a simplified version of JK flip-flop. The T flop is obtained by connecting the J and K inputs together. The flip-flop has one input terminal and clock input. These flip-flops are said to be T flip-flops because of their ability to toggle the input state. Toggle flip-flops are mostly used in counters.

Truth Table of T Flip-Flop

T	Q(t)	Q(t+1)
0	0	0
0	1	1
1	0	1
1	1	0

Characteristics Equation of T Flip-Flop

$$\mathrm{Q(t \: + \: 1) \: = \: T'Q(t) \: + \: TQ(t)' \: = \: T \: \oplus \: Q(t)}$$

Applications of Flip-Flops

Counters
Shift Registers
Storage Registers, etc.

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