# SR Flip Flop- Truth Table and Characteristic Equation

Last Updated on July 7, 2023 by Electricalvolt

The SR Flip-Flop has two inputs( S &R) and two outputs( Q & Q’). It is also called a gated or clocked SR latch. It temporarily stores the information of one bit.

In digital electronics, a flip-flop (FF) is a 1-bit storage device. It is also known as a bistable multivibrator as it has two stable states, denoted by 0 and 1. Based on construction, FFs are classified into various types such as SR, JK, D, and T flip-flops.

## What is an SR FlipFlop?

An SR flip-flop is one which has two inputs namely “set” and “reset”, which are denoted by “S” and “R” respectively.  SR FF is a clocked or gated SR latch that can store 1-bit of binary information.

The block diagram of an SR FF is depicted in the following figure.

It has three input lines namely S, R, and CLK, and two output lines viz. Q and Q’. Where S and R are the binary inputs of the circuit, and CLK is the clock input. The Q is the normal output of the SR flip flop, while Q’ is the complemented output, i.e. it is inversion of the normal output.

## SR FlipFlop Circuit Diagram

We can construct SR FF using either NOR latch or NAND latch. The circuit diagrams of these two constructions are shown below.

### (1). SR FlipFlop using NOR Latch:

The logic circuit diagram of an SR FF using NOR latch is illustrated in the following figure

### (2). SR FlipFlop using NAND Latch:

The logic circuit diagram of an SR FF using a NAND latch is shown in the following figure.

## SR Flip Flop Characteristic Table

The characteristic table of an SR flip-flop is used to understand the behavior of an SR FF for different input combinations of S and R inputs for other clock transitions.

The following is the characteristic table of an SR FF.

## Truth Table of SR Flip Flop

The truth table of an SR flip-flop is nothing but the version of the characteristic table. It provides information about the operation of the SR FF for different input combinations.

SR flip-flop truth table is given below.

## Characteristic Equation of SR Flip-Flop

The characteristic equation of an SR flip-flop is a logical expression that specifies the relationship between inputs S and R, and output Qn+1. We can derive the characteristic equation of SR FF by using its characteristic table and k-map simplification method.

The k-map simplification for the next state, i.e. Qn+1 of SR FF is given below.

On simplification of this k-map, we get the following expression,

This expression is known as the characteristic equation of SR flip-flops.

SR FF offers the following some major advantages over other types of flip-flops:

• The logic circuit of an SR FF is quite simple to construct and analyze.
• It provides higher speed which makes it a better choice for high-speed digital devices.
• It consumes very low power which makes it a better option for battery-powered devices.
• SR flip-flops provide a bistable operation that allows it to hold its one state infinitely.

## Limitations

SR FF has several benefits, but it also has some limitations. A few major limitations of SR flip-flops are listed below:

• When both inputs, i.e. S and R are activated at the same time, the flip-flop goes into the invalid state.
• SR flip-flops cannot be used to implement highly complex digital systems due to the high probability of errors.
• It can have race-around conditions that can change the output states unpredictably.

## Applications of SR Flip-Flops

SR flip-flops are widely used in various digital systems. Some common uses are listed below:

• SR flip-flops are used in various digital memory devices like registers, cache, RAM, etc. to store binary information.
• SR flip-flops are also used in digital counter circuits to count events.
• SR flip-flops can also be used for data synchronization among digital systems.
• SR flip-flops are also used in digital control systems.

Hence, this is all about the SR flip-flop, its construction, truth table, advantages, limitation, and applications.