Digital Logic Design Lecture 9

i# Digital Logic Design Lecture 9 This Lecture covers unit 2 beginning. and the index as follows

Comparison between Analog and Digital systems

Digital Logic Design Analogue and Digital Systems

Details Roll Number : K057 Name : Tejas Kamal Sahoo Branch : Btech Cyber Security Year : 2nd Semester : 2 Due Date : 29-7-2024 Date & Time : 28-07-2024 11:57

Main note

Digital Signals and Analogue Signals

Analogue Signals

• Nature: Continuous and smooth variations over time.
• Representation: Represented by continuous waveforms such as sine waves.
• Characteristics:
  • Infinite range of values within a given range.
  • More susceptible to noise and distortion.
  • Commonly used in audio and video transmissions, radio signals, and analog recordings.

Digital Signals

• Nature: Discrete and consist of distinct levels or steps.
• Representation: Represented by binary values (0 and 1) and square waves.
• Characteristics:
  • Finite range of values, typically only two (0 and 1).
  • Less susceptible to noise; more reliable for long-distance transmission.
  • Commonly used in computing, digital communications, and digital storage.

Use of Binary in Digital Systems

Why Use Binary?

1. Simplicity:
   • Digital systems are simpler to design and implement using binary (0 and 1) because only two states need to be recognized and processed.
2. Reliability:
   • Binary signals are less prone to errors and noise compared to analog signals. Distinguishing between two distinct states (on/off, 0/1) is more reliable than detecting a range of values.
3. Compatibility with Digital Electronics:
   • Digital circuits and microprocessors inherently operate using binary logic (transistors act as switches that can be either on or off).
4. Data Processing:
   • Binary data is easily processed by digital systems, enabling efficient arithmetic operations, logic operations, and data storage.

How We Use Binary in Digital Systems

1. Representation:
   • Binary values represent data and instructions in computers and digital devices. Each bit (binary digit) is either a 0 or a 1.
2. Storage:
   • Binary data is stored in memory devices (e.g., RAM, SSDs) and storage media (e.g., hard drives, flash drives) using binary encoding.
3. Transmission:
   • Binary signals are used for data transmission in digital communication systems, including the internet, telecommunication, and networking.
4. Processing:
   • Central Processing Units (CPUs) and other digital processors perform computations and operations using binary logic and binary arithmetic.
5. Analog-to-Digital Conversion (ADC):
   • Converts analog signals to digital signals for processing. For example, audio input (analog) is converted to digital for storage and manipulation in digital devices.
6. Digital-to-Analog Conversion (DAC):
   • Converts digital signals back to analog signals for output. For example, digital audio files are converted to analog signals for playback through speakers.

Analogue and Digital Counterparts

• Analog Devices:
  • Use continuous signals to represent information. Examples include traditional radios, vinyl record players, and analog watches.
• Digital Devices:
  • Use binary signals for representation and processing. Examples include computers, smartphones, digital watches, and digital cameras.

By using binary systems, digital devices achieve high reliability, efficiency, and compatibility with digital technology, enabling the vast array of modern digital applications and innovations.

Comparison of Analogue vs Digital Signals

Feature	Analogue Signals	Digital Signals
Nature	Continuous signals that vary smoothly over time.	Discrete signals that vary in steps or levels.
Representation	Represented by sine waves.	Represented by square waves or binary values (0, 1).
Signal Range	Infinite range of values within a given range.	Finite range of values (often just 0 and 1).
Noise Sensitivity	More susceptible to noise and distortion.	Less susceptible to noise; more reliable.
Bandwidth	Can be high, depending on the signal.	Generally requires less bandwidth.
Transmission	Prone to signal degradation over long distances.	Can be transmitted over long distances without much degradation.
Hardware	Analog hardware is complex and often more expensive.	Digital hardware is simpler and often cheaper.
Accuracy	Can be more accurate but harder to process.	Easier to process but can be less accurate.
Applications	Used in audio and video transmission, radio signals.	Used in computing, digital communications, and storage.
Conversion	Analog-to-Digital Converter (ADC) needed for digital processing.	Digital-to-Analog Converter (DAC) needed for analog outputs.

References

Information

• date: 2024.07.30
• time: 11:57

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Symbols for Logical Operations

Function	Representation	Name
AND	$A\wedge B$ or $A\cdot B$	AND Gate
OR	$A\vee B$ or $A+B$	OR Gate
NAND	$\overline{A\wedge B}$	NAND Gate
NOR	$\overline{A\vee B}$	NOR Gate
XOR	$A\oplus B$	XOR Gate
XNOR	$\overline{A\oplus B}$	XNOR Gate
NOT	$\overline{A}$	NOT Gate (Inverter)
NAND (3-input)	$\overline{A\cdot B\cdot C}$	3-Input NAND Gate
OR (3-input)	$A\vee B\vee C$	3-Input OR Gate

Types of Circuits

There are mostly two types of circuits that we will be covering in unit 2.

Combinational Circuits

Combinational circuits are logic circuits where the output depends solely on the current inputs. They do not have memory or feedback loops, meaning the output is a direct function of the inputs at any given time. These circuits perform operations such as addition, subtraction, and encoding based on the input values.

Key Characteristics:

• No Memory: The output is purely a function of the current input values. There is no storage of previous input states.
• Immediate Response: The output changes as soon as the input changes, reflecting the combinational logic of the circuit.

Components

1. Set of statements
2. Boolean expression
3. Truth Table

Sequential Circuits

Sequential circuits are logic circuits where the output depends on both the current input and the history of inputs. This means they have memory elements like flip-flops or latches to store previous states. The output is a function of the current inputs and the stored state.

Key Characteristics:

• Memory: Sequential circuits have memory elements that store information about past inputs or states.
• Clock-Driven: Many sequential circuits are synchronized with a clock signal that controls when the memory elements are updated.

Simplification of the Boolean Functions

1. Algebraic Method
2. Karnaughh-map technique ( K-Map )
3. Quine McCluskey Method and
4. Variable entered mapping

Algebraic Method

For example

$$Y=(A+BC)(B+\overline{C}A)$$ $$Y=A\cdot (B+\overline{C}A)+BC\cdot (B+\overline{C}A)$$ $$Y=A\cdot B+A\cdot \overline{C}A+BC\cdot (B+\overline{C}A)$$ $$Y=A\cdot B+A\cdot \overline{C}+BC\cdot B+BC\cdot \overline{C}A$$ $$Y=A\cdot B+A\cdot \overline{C}+BC$$

Product of Sums (POS)

Consider the Boolean function ( F(A, B, C) ) which can be represented in the POS form as follows:

$$F(A,B,C)=(\overline{A}+\overline{B}+\overline{C})(A+B+C)$$

Sum of Products (SOP)

Consider the Boolean function ( F(A, B, C) ) which can be represented in the SOP form as follows:

$$F(A,B,C)=\overline{A}BC+AB\overline{C}$$

Basic Logic Operation using NAND Gate

Unindexed

Digital Signal Representation

Positive Logic

Using a high signal for high ( Binary 1 ) and low voltage for low signal ( Binary 2 ).

Negative Logic

Using a low signal for high ( Binary 1 ) and high voltage for low ( Binary 2 ).

References

Information

• date: 2024.08.13
• time: 13:10