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Showing posts with label DIGITAL ELECTRONICS. Show all posts
Showing posts with label DIGITAL ELECTRONICS. Show all posts

Wednesday, October 6, 2021

October 06, 2021

Full Adder Circuit with Truth Table-Block diagram-Circuit diagram


Full Adder: The half adder is used to add only two numbers. To overcome this problem, the full adder was developed. The full adder is used to add three 1-bit binary numbers A, B, and carry C. The full adder has three input states and two output states i.e., sum and carry.

Block diagram



Truth Table



 1. 'A' and 'B' are the input variables. These variables represent the two significant bits which are going to be added
2. 'Cin' is the third input which represents the carry. From the previous lower significant position, the carry bit is fetched.
3. The 'Sum' and 'Carry' are the output variables that define the output values.
4. The eight rows under the input variables designate all possible combinations of 0 and 1 that can occur in these variables.

The SOP form can be obtained with the help of K-map as:
Hence, from K-maps,







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Saturday, February 6, 2021

February 06, 2021

Half Adder in Digital Logic


Half Adder

A Half Adder is defined as a basic four terminal digital device which adds two binary input bits. It outputs the sum binary bit and a carry binary bit.

Block diagram
Truth Table:

Explanation:

As we have defined above, a half adder is a simple digital circuit used to digitally add two binary bits. A binary bit is either 0 or 1. Hence, there will be four addition combinations these two binary digits and those will be 0+0, 0+1, 1+0 and 1+1.
We know that decimally:
Again, we know that decimal 2 can be represented in two bits binary system as 1 0 (One Zero). Binary two is the smallest double digits number in the binary system. When we add binary 1 with binary 1 we will get both sum and carry since 10 is two digits binary number. When we add 0 to 0, 0 to 1, 1 to 0, we get the sum 0 and 1 respectively and both of them are one digit binary number. Hence, in these  three cases there will be no carry during addition or carry is 0 here. We can summarise this in a truth table for the half adder.

Half Adder Truth Table:


From the above truth table, we can see that the sum digit of two binary inputs is the outcome of XOR operation and we can realize it by using an XOR gate.
Carry digit of those two binary inputs is the outcome of AND operation and we can realize it by an AND gate.

Half-Adder logical circuit:

So, the Half Adder is designed by combining the 'XOR' and 'AND' gates and provide the sum and carry.
There is the following Boolean expression of Half Adder circuit:


This set of Digital Electronics/Circuits Multiple Choice Questions & Answers (MCQs) focuses on "Half Adder"

1. In parts of the processor, adders are used to calculate ___________





View Answer = (D) All of the Mentioned
Explanation:- Adders are used to perform the operation of addition. Thus, in parts of the processor, adders are used to calculate addresses, table indicess, increment and decrement operators, and similar operations.

2. Half-adders have a major limitation in that they cannot _________





View Answer = (c) Accept a carry bit from a previous stage
Explanation:- Half-adders have a major limitation in that they cannot accept a carry bit from a previous stage, meaning that they cannot be chained together to add multi-bit numbers. However, the two output bits of a half-adder can also represent the result A+B=3 as sum and carry both being high.

3. If A and B are the inputs of a half adder, the carry is given by _________





View Answer = (A) A AND B
Explanation:- If A and B are the inputs of a half adder, the carry is given by: A(AND)B, while the sum is given by A XOR B.
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Wednesday, January 22, 2020

January 22, 2020

Digital Electronics Syllabus 2021

  • Boolean Algebra and Logic Gates :

1. Properties of Boolean algebra
2. Representation of Boolean Functions
3. Canonical and Standard Form
4. Functional Completeness
5. Logic Gates
  • Gate Level Minimization :

1. K-Map(Karnaugh Map)
2. Implicants in K-Map
3. 5 variable K-Map
4. Variable entrant map (VEM)
5. Minimization of Boolean Functions
6. Consensus theorem

2. Half-Subtractor
3. Half-Adder and Half-Subtractor using NAND NOR Gates
4. Full-Adder 
5. N-Bit Parallel Adder
5. Half Subtractors
5. Full Subtractors
6. Code Converters - BCD(8421) to/from Excess-3
7. Code Converters - Binary to/from Gray Code
8. Code Converters - BCD to 7 Segment Decoder
9. Parallel Adder & Parallel Subtractor
10. Carry Look-Ahead Adder
11. Magnitude Comparator
12. BCD Adder
13. Encoders and Decoders
14. Encoder
15. Binary Decoder
16. Combinational circuits using Decoder
17. Multiplexers
18. Static Hazards
  • Flip-Flops and Sequential Circuits :

1. Latches
2. One bit memory cell
3. Flip-Flops(Types and Conversions)
4. Master Slave JK Flip Flop
5. Introduction of Sequential Circuits
6. Synchronous Sequential Circuits
7. Asynchronous Sequential Circuits
8. Difference between combinational and sequential circuit
9. RTL (Register Transfer Level) design vs Sequential logic design
10. Difference between Synchronous and Asynchronous Sequential Circuits
  • Memory and Programmable Logic :

1. Read-Only Memory (ROM) | Classification and Programming
2. Programmable Logic Array
3. Programming Array Logic
4. RAM vs ROM
 5. Operational Amplifier (op-amp)

  • Register and Counters:

1. Counters
2. Design counter for given sequence
3. n-bit Johnson Counter
4. Amortized analysis for increment in counter
5. Ripple Counter 
6. Digital Logic | Ring Counter
7. Shift Registers
8. Design 101 sequence detector
9. Universal Shift Register
10. RTL (Register Transfer Level) design vs Sequential logic design
11. Verilog Data Types
  • Data Communication :

1. Block Coding
2. Difference between Unipolar, Polar and Bipolar Line Coding
3. Difference between Broadband and Baseband Transmission
4. Transmission Impairment
5. What is Scrambling?
6. Analog to Analog Conversion (Modulation)
7. Analog to digital conversion 8. Digital to Analog Conversion
 9. Difference Between Digital And Analog System


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Friday, January 10, 2020

January 10, 2020

Digital Electronics | Number System And Codes

INTRODUCTION
In this modern world of electronics, the term digital is mostly associated with a computer. Number systems are used to represent data in digital systems. In this chapter, we will consider the following topics:
  • Analog and digital system.
  • Number systems: decimal, binary, octal, and hexadecimal number systems 
  • Counting in various number systems 
  • Number system conversions 
  • Basic binary arithmetic: addition, subtraction, multiplication, division. 
  • Complements of numbers: 1's and 2's complement of binary number, 7's and 8's complement of octal number, 9's and 10's complement of decimal number, 15's and 16's complement of hexadecimal number. 
  • Number representation in binary system: sign magnitude representation, 1's complement representation, 2's complement representation.
  • Complement binary, octal, decimal, and hexadecimal arithmetic: addition and subtraction using complement of numbers.
  • Binary codes: BCD, Excess-3 code, Gray code; their conversion.
Analog and digital systems
There are two types of electronic circuits and systems:
Analog System: Analog systems are those in which physical quantities are represented over a continuous range of values.
Digital System: Digital systems are those in which physical quantities are represented in digital form; that is, the quantities can take on only discrete values.
The comparison between analog and digital system are given in the following text

Advantages of Digital System
1. Digital systems are easier to design.
2. Storage of information is easy.
3. Greater accuracy and precision.
4. Digital systems are less affected by noise.  5.Operation can be controlled by a program.
6. More digital circuitry can be fabricated on integrated circuit (IC) devices.
7. Digital Systems are more reliable.

Limitations of Digital System
In real world, most physical quantities are analog in nature. These quantities are used as input signals of system and monitored for controlling the system. In digital system, these analog quantities are converted to digital quantities. Because of these conversions, the processing time increases and the system becomes more complex.

Number system
A number system is nothing more than a code that uses symbols to represent a number. In general, in any number system, there is an ordered set of symbols known as digits. A number is made up of a collection of digits and it has two parts; integer and fraction, both are separated by a radix point (.). The number is represented as,


 Where, r = radix or base of the number system n= number of digits in the integer part
m = number of digits in fractional part
dn-1= most significant digit (MSD)
d-m= least significant digit (LSD) On the basis of number of different symbols used (radix), number systems are classified as
1. Decimal number system
2. Binary number
3.Octal number system
4. Hexadecimal number system
Now, we discuss each number system in following sections.


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Wednesday, January 8, 2020

January 08, 2020

Digital Electronics| Combinational Logic Circuit-definition,truth table ,block diagram

INTRODUCTION
Generally, digital circuits are divided into two categories: combinational logic circuit and sequential logic circuit.

The combinational logic circuits are the circuits that contain different types of logic gates. Simply, a circuit in which different types of logic gates are combined is known as a combinational logic circuit. The output of the combinational circuit is determined from the present combination of inputs, regardless of the previous input. The input variables, logic gates, and output variables are the basic components of the combinational logic circuit. There are different types of combinational logic circuits, such as Adder, Subtractor, Decoder, Encoder, Multiplexer, and De-multiplexer.

This chapter, concerned with the study of combinational circuit, includes the following topics:
Combinational Logic Circuit Definition
the combinational logic circuits or time-independent logic circuits in digital circuit theory can be defined as a type of digital logic circuit implemented using Boolean circuits, where the output of logic circuit is a pure function of the present inputs only. The combinational logic circuit operation is instantaneous and these circuits do not have the memory or feedback loops.
This combinational logic is in contrast compared to the sequential logic circuit in which the output depends on both present inputs and also on the previous inputs. Thus, we can say that combinational logic does not have memory, whereas sequential logic stores previous input in its memory. Hence, if the input of combinational logic circuit changes, then the output also changes.
The combinational logic design can be done using two methods such as a sum of products and a product of sums. Combinational logic circuits are generally designed by connecting together or combining the basic logic gates such as NAND, NOR, and NOT. Hence, these logic gates are termed as building blocks. These logic circuits can be a very simple circuit or a very complex circuit or huge combinational circuit can be designed using only universal logic gates 
DESIGN PROCEDURE FOR COMBINATION LOGIC CIRCUITS 
There are the following characteristics of the combinational logic circuit:
  • At any instant of time, the output of the combinational circuits depends only on the present input terminals.
  • The combinational circuit doesn't have any backup or previous memory. The present state of the circuit is not affected by the previous state of the input.
  • The n number of inputs and m number of outputs are possible in combinational logic circuits.

The 'n' input variable comes from the external source while the 'm' output variable goes to the external destination. In many applications, the source or destinations are storage registers.

The steps used to design a combinational logic circuit using gates are:
METHODOLOGY: DESIGNING A COMBINATIONAL LOGIC CIRCUITS 
Step 1: Statement of the problem.
Step 2: Identify the input and output variables.
Step 3:The input and output variables are assigned letter symbols.
Step 4:Construct a truth table that defines the required relationship between inputs and outputs is derived.
Step 5:Write Boolean expressions for various output variables in terms of input variables.
Step 6: Simplify the Boolean expression using K-map or Quine- McCluskey method.
Step 7: Implement the simplified Boolean expressions using logic gates.
FUNCTIONS OF COMBINATIONAL LOGIC CIRCUIT
The function of combinational logic circuits can be specified in three main ways such as:
  • Boolean Algebra: This forms the algebraic expression showing the operation of the logic circuit for each input variable either True or False that results in a logic "1" output.
  • Truth Table: A truth table defines the function of a logic gate by providing a concise list that shows all the output states in tabular form for each possible combination of input variable that the gate could encounter.
  • Logic Diagram: This is a graphical representation of a logic circuit that shows the wiring and connections of each individual logic gate, represented by a specific graphical symbol, that implements the logic circuit.



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