Decoder and Multiplexer

2023. July 31

encoding, for computer

decoding, for human

Decoder

1. Key Features and Working of a Decoder:

1) a decoder has 'n' input lines and 2^n output lines

2) input to the decoder is a binary code represented by 'n' bits. Each input combination uniquely selects one of the output lines.

3) Only one output line will be active (high) at a time on the binary code applied to the input.

4) The decoder's truth table is based on the binary representation of the input lines and their corresponding outputs.

* 3-to-8 Decoder example

2. Applications of Decoders

1. Memory Address Decoding: In computer memory systems, decoders are used to convert the binary memory address to a specific memory location. This enables the selection of particular memory cell from a large memory array.

2. Digital Display Systems: In digital display applications, such as 7-segment displays, decoders are used to convert binary-coded input to the corresponding display segments' activation.

3. Control Signal Decoding: Decoders are used in control systems to interpret binary control signals and activate specific devices or perform specific actions based on the input code.

4. Demultiplexing: In data routing, decoders are used to demultiplex a single input line to one of several output lines based on the input code.

5. Instruction Decoding: In microprocessors, decoders are used to interpret instruction codes and generate control signals for executing various instructions.

Encoder

1. Key Features and Working of an Encoder:

1) An encoder has 'n' input lines and 'm' output lines. The number of output lines is generally smaller than the number of input lines.

2) The encoder produces a binary code at the output, representing the active input line

3) Only one input line should be active (high) at a time an encoder. If multiple input lines are active, the encoder will prioritize one of them.

2. Application of Encoders

1) Priority Encoding: Encoders are used to encode multiple inputs into a priority-encoded format. In applications where only the highest-priority input needs to be encoded, and the rest are ignored, priority encoders are utilized.

2) Address Encoding: In memory systems, encoders are used for memory address encoding, converting the binary address lines into a compact binary code used to select a specific memory location. 

3) Data Transmission: Encoders are used in digital communication systems to encode data for transmission over communication channels

4) Digital Control Systems: Encoders are used in digital systems to encode the states of sensors, switches, or other input devices into a binary code.

01_1) Introduction to Boolean Algebra

 2 possible values, typically represented as true (1) or False (0).

These binary values are essential in digital circuits, as they form the foundation for decision-making and information processing.

* Basic Concepts:

1. Boolean Variables: 0 or 1, false or true, low or high, etc.

2. Logical Operation: Basic logical operations: AND, OR, and NOT.

1) AND: produces an output of 1 only if both A and B are 1. Otherwise, the output is 0.

2) OR: produces an output of 1 only if either A or B (or both) are 1. The output is 0 only if both A and B are 0.

3) NOT: inverts its value.

3. Boolean Expressions: combinations of variables and logical operators. They represent complex logical conditions. For example A and B, A or B, not A

4. Truth Tables: truth tables are used to show the outputs of a Boolean expression for all possible combinations of inputs. They help in understanding the behavior of logical functions and verifying their correctness. 

* Boolean Laws and Theorems:

Boolean Algebra follows a set of laws and theorems that enable the simplification and manipulation of expressions. Some essential laws include:

1. Commutative Law: a and b = b and a, a or b = b or a

2. Associative Law:  (a and b) and c = a and (b and c)

3. Distributive Law: a and (b or c) = (a and b) or (a and c)

4. Identity Law: the AND identity is 1, and the OR identity is 0.

5. Complement Law: A AND NOT A = 0, A OR NOT A = 1

* Applications:

Boolean Algebra plays a crucial role in various applications, including:

- Designing and analyzing digital logical circuits.

- Creating logical expressions for programming and software development.

- Developing decision-making systems and control circuits.

- Circuit optimization to reduce complexity and power consumption.

Digital System Design Contents

 1. Boolean Algebra

Introduction to Boolean Algebra

Basic Logic Operations: AND, OR, NOT

Boolean Expressions and Truth Tables

Logic Simplification using Boolean Laws

De Morgan's Theorem

2. Combinational Logic

Overview of Combinational Logic

Logic Gates and their Applications

Combinational Circuit Design Process

Multiplexers and Demultiplexers

Encoders and Decoders

Adders and Subtractors

3. Sequential Logic: Flip-flops, Clocking

Introduction to Sequential Logic

Latches vs. Flip-Flops

SR, D, JK, and T Flip-Flops

Timing and Clock Signals

Synchronous vs. Asynchronous Sequential Circuits

4. Programmable Logic

Introduction to Programmable Logic Devices (PLDs)

Complex Programmable Logic Devices (CPLDs)

Field-Programmable Gate Arrays (FPGAs)

Advantages and Applications of PLDs

HDLs for Programmable Logic Design (VHDL/Verilog)

5. Finite State Machines: Implementation & Optimization

Understanding Finite State Machines (FSMs)

Mealy vs. Moore FSMs

State Diagrams and State Tables

FSM Design Process

Optimization Techniques for FSMs

6. Memory Organization

Overview of Memory Units

Random Access Memory (RAM) Types

Read-Only Memory (ROM) Types

Cache Memory and Its Importance

Memory Interfacing Techniques

7. Computer Arithmetic

Number Systems (Binary, Decimal, Hexadecimal)

Binary Addition and Subtraction

Binary Multiplication and Division

Two's Complement Representation

Arithmetic Logic Unit (ALU)

8. Microprocessor-based System Design

Introduction to Microprocessors

Microprocessor Architecture and Components

Instruction Set and Assembly Language

Memory and I/O Interfacing with Microprocessors

Overview of Embedded Systems