INTRODUCTION ABOUT DIGITAL SYSTEMS

Digital system is an interconnection of digital modules and it is a system that manipulates discrete elements of information that is represented internally in the binary form.

Now a day’s digital systems are used in wide variety of industrial and consumer products such as automated industrial machinery, pocket calculators, microprocessors, digital computers, digital watches, TV games and signal processing and so on.

Characteristics of Digital systems

•Digital systems manipulate discrete elements of information.

•Discrete elements are nothing but the digits such as 10 decimal digits or 26 letters of alphabets and soon.

•Digital systems use physical quantities called signals to represent discrete elements.

•In digital systems, the signals have two discrete values and are therefore said to be binary.

•A signal in digital system represents one binary digit called a bit. The bit has a value either 0 or1.

Analog systems vs Digital systems

Analog system process information that varies continuously i.e; they process time varying signals that can take on any values across a continuous range of voltage, current or any physical parameter.

Digital systems use digital circuits that can process digital signals which can take either 0 or 1 for binary system.

Advantages of Digital system over Analog system

1. Ease of programmability The digital systems can be used for different applications by simply changing the program without additional changes in hardware.

2. Reduction in cost of hardware The cost of hardware gets reduced by use of digital components and this has been possible due to advances in IC technology. With ICs the number of components that can be placed in a given area of Silicon are increased which helps in cost reduction.

3.High speed Digital processing of data ensures high speed of operation which is possible due to advances in Digital Signal Processing.

4. High Reliability Digital systems are highly reliable one of the reasons for that is use of error correction codes.

5. Design is easyThe design of digital systems which require use of Boolean algebra and other digital techniques is easier compared to analog designing.

6. Result can be reproduced easily Since the output of digital systems unlike analog systems is independent of temperature, noise, humidity and other characteristics of components the reproducibility of results is higher in digital systems than in analog systems.

Disadvantages of Digital Systems

•Use more energy than analog circuits to accomplish the same tasks, thus producing more heat as well.

•Digital circuits are often fragile, in that if a single piece of digital data is lost or misinterpreted the meaning of large blocks of related data can completely change.

•Digital computer manipulates discrete elements of information by means of a binary code.

•Quantization error during analog signal sampling.

Logical Gates

Logical gates are important building blocks in digital circuits. So study of logic gates is very important. There are three types of basic gates. AND, OR and NOT gates. Other gates are NAND, NOR, EX-OR, EX-NOR etc. English mathematician George Boole invented symbolic logic in 1854, which is known as Boolean Algebralogic levelsThere are two types of Logic levels : 0 and 1. These show quite different situation as shown in the following table.

Sr.No Device Logic 0 Logic 1 1 Switch Off On2 Door Closed Open3 Lamp Off On4 Level Low High

Logic Gates :

Gates is an electronic ckt with one or more inputs but only one output.

Logic gates process signals which represent true or false.

Logic gates are blocks of hardware that produce a logical 1 or logical 0 output signal depending on input signal to logic gate.

They are also known as logic circuit because with the proper

input they establish logical manipulation path.

Logic Gates :

They also categorized as below

(1)Basic gates-(AND, OR, NOT)

(2)Universal gates-(NAND, NOR)

(3)Exclusive gates-(EX-OR, EX-NOR)

Combinational Circuits :It is logical circuits, the output at any time depends on the logic levels at the input at that instant only.

It does not depend on the past condition.

A combinational circuit transforms binary information from the given output data to the required output data

Half Adder :A half adder is a combinational circuit adds two binary bits.Block diagram of half adder is as given below.

There are two input terminals which are marked as A and B.Binary numbers the sum of which has to be made are applied here.There are two output terminals. One terminal is for sum and the other is the carry bit C.Truth table of half adder is shown below.

0+0 = 000+1 = 011+0 = 011+1 = 10

Sum= A XOR BCarry = A AND B

HA Logical Diagram

Full Adder :A full adder is a combinational circuit that performs the arithmetic sum of three input bits.It consists three inputs and two outputs.When we want to add two binary numbers each having two or more bits the LSB (Least Significant Bit) can be added by using a half adder.Block diagram of full adder is as given below:

In this there are three input terminal. One output is Ci which is carry from the previous stage.A and B are two input terminals. There are two output terminals. One is final sum S and the other is final carry C.

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Combinational Logic circuits that change state depending upon the actual signals being applied to their inputs at that time, 

Sequential Logic circuits have some form of inherent “Memory” built in.

This means that sequential logic circuits are able to take into account their previous input state as well as those actually present, a sort of “before” and “after” effect is involved with sequential circuits.In other words, the output state of a “sequential logic circuit” is a function of the following three states, the “present input”, the “past input” and/or the “past output”. Sequential Logic circuits remember these conditions and stay fixed in their current state until the next clock signal changes one of the states, giving sequential logic circuits “Memory”.Sequential logic circuits are generally termed as two state or Bistable devices which can have their output or outputs set in one of two basic states, a logic level “1” or a logic level “0” and will remain “latched” (hence the name latch) indefinitely in this current state or condition until some other input trigger pulse or signal is applied which will cause the bistable to change its state once again.

Sequential Logic Representation

The word “Sequential” means that things happen in a “sequence”, one after another and in Sequential Logic circuits, the actual clock signal determines when things will happen next. Simple sequential logic circuits can be constructed from standard Bistable circuits such as: Flip-flops, Latches and Counters and which themselves can be made by simply connecting together universal NAND Gates and/or NOR Gates in a particular combinational way to produce the required sequential circuit.

Sequential Circuit :

Digital electronics is classified into combinational logic and sequential logic.Combinational logic output depends on the input levels whereas sequential logic output depends on sorted level and also the input levels.The memory element are devices capable of storing binary info.The binary info stored in the memory elements at any given time defines the state of the sequential circuit.

There are two types of sequential circuit.

Their classification depends on the timing of their signals.•Synchronous sequential circuits•Asynchronous sequential circuits

In order to build sophisticated digital logic circuits, including computers, we need more a powerful model.We need circuits whose output depends upon both the input of the circuit and its previous state.

In other words we need circuits that have memory.Flip-Flop :A Flip-Flop is a binary cell capable for storing just one bit of information. i.e. they contain either 0 or 1.

It is kind of an electronic circuit which has two stable states, therefore it is also known

as bistable multivibrator,and thereby is capable of serving as one bit of memory.

In other words a sequential circuit is an interconnection of flip-flop and gates.

The gates by themselves constitute a combinational circuit, but when included with flip-flop the overall circuit is classified as a sequential circuit.It has two output terminals which are complement of each other. Which are Q and Q’.When Q is at logic 0, flip flop is at reset and when Q is at logic = 1 it is in set mode.

They are various FF available which are...(1) SR or RS FF (2) D FF

(3) T FF(4) JK FF(5) Master slave JK FF