Module 1 Slides Digital Information and Computing 1 Binary Number Representation Conversion Equations Decimal to Binary Repeated division by 2 Binary to Decimal Sum of powers of 2 2 von Neumann Architecture Key Principle Instructions and data stored in the same memory Enables programs to generate other programs Foundation of modern computer design 3 Processor Operation Components Arithmetic Logic Unit ALU Performs computations Processor synchronized by clock cycles 4 Algorithm Complexity Complexity Measurement Growth of computation time relative to problem size Example Prime Number Counting Algorithms Naive method Sieve of Eratosthenes 5 Artificial Intelligence Principles Two Phase Operation Training Learning from examples Inference Applying learned knowledge Example Probabilistic word prediction Relies on statistical pattern matching rather than understanding Module 2 Sampling and Quantization 1 Signals and Processing A signal is a time dependent variation used to convey information Signal processing transforms signals to extract or produce meaningful data Fourier Representation Any signal can be represented as a sum of sinusoids with different frequencies 2 Key Techniques Nyquist Sampling Theorem i Definition To digitize a continuous signal without distortion aliasing the sampling rate must be at least twice the signal s highest frequency component This minimum rate is called the Nyquist rate ii Nyquist Frequency Half the sampling rate This represents the maximum frequency that can be captured accurately iii Aliasing When the sampling rate is too low high frequency components get misrepresented as lower frequencies iv Formula fs 2 fmax where fs is the sampling rate and fmax is the highest frequency component v Applications 1 Audio CD quality audio uses a 44 1 kHz sampling rate to capture frequencies up to 20 kHz 2 Imaging Sampling rates must exceed twice the maximum spatial frequency to avoid visual distortions Quantization values i Process Converts continuous analog signal levels into discrete digital 1 Analog signal is sampled at discrete intervals 2 Each sample is assigned a discrete value ii Resolution Determined by the number of bits n in the ADC 1 2 n levels available 2 Higher bit depth results in finer resolution and greater fidelity iii Quantization Noise levels 1 The error is introduced by mapping continuous values to discrete 2 Increasing resolution decreases noise power iv Signal to Quantization Noise Ratio SQNR 1 Measures the quality of the digital signal a SQNR 4 n b SQNRdB 6n dB 2 Every additional bit improves SQNR by 6 dB i Goal Reduce data size by eliminating redundant or unnecessary Compression information ii Types 1 Lossless Compression Original data recovery e g ZIP FLAC 2 Lossy Compression Discards less noticeable information using perceptual models e g MP3 JPEG iii MP3 Example 1 Uses psychoacoustics e g auditory masking 2 Removes frequencies humans cannot perceive under certain conditions reducing file size iv Applications 1 Analog to digital ADC and Digital to Analog Conversion DAC are foundational in systems like MP3 players 2 MP3 encoding involves spectrum analysis Discrete Fourier Transform and compression using perceptual models Module 3 Power 1 Basic Concepts 2 Power Systems Power P Voltage V Current I Energy Power Time Power is the rate of energy transfer Generation Electric power derived from various sources like hydro solar nuclear etc Transmission High voltage systems minimize losses P loss I R Distribution Transformers step down voltage for consumer use Solar Power Efficiency determined by material and conditions Advanced systems use Maximum PowerPoint Trackers MPPT for optimization Power grids require constant balancing between supply and demand 3 Efficiency 4 Historical Trends Koomey s Law i Definition Describes improvements in computational energy efficiency Historically the number of computations per joule of energy doubled approximately every 1 57 years ii Post 2010 Trends to limitations in 1 Efficiency improvements slowed to a doubling every 2 6 years due a Moore s Law Smaller transistors b Dennard Scaling Shrinking transistors with constant iii Implications power density 1 Innovations like low power hardware and specialized architectures e g GPUs are crucial to sustaining efficiency growth Smart grids and renewable energy integration are transforming traditional Real time market pricing ensures efficient distribution based on demand and 5 Electricity Market systems supply 6 Power Systems Basic Formulas i Power P V I ii Energy E P t R Renewable Energy Transmission High voltage systems reduce power losses since P loss I 2 i Solar Efficiency depends on light intensity and material ii Systems use Maximum Power Point Trackers MPPTs to optimize output Comparison Koomey s vs Moore s Law Aspect Koomey s Law Focus Energy Efficiency Moore s Law Transistor density Timeframe Doubling 1 57 years historically Doubling 2 years historically Current Trends Slowed to 2 6 years Facing physical constraints Module 4 Computer Hardware 1 Hardware Design and Optimization Structured design emphasizes modularity regularity and hierarchical approaches e g MIPS architecture Amdahl s Law Overall speedup is limited by the fraction of the process that benefits from the enhancement 2 Digital Logic Logic gates AND OR NOT form the foundation of digital systems CMOS transistors act as switches NAND and NOR gates are critical for circuit design 3 Fabrication Trends improvements 4 Hardware Metrics consumption 5 Applications Moore s Law Transistor density doubles every two years driving performance Fabrication materials Transition from aluminum to copper for better conductivity Performance is measured by speed GHz energy efficiency and power Parallel processing and larger caches improve computational power Modern processors e g Intel i9 12900K emphasize multi core designs and GPUs like NVIDIA RTX 4090 showcase high parallelism and efficiency for on chip caches for speed specialized tasks Module 5 Electromagnetic Signals and Communication Systems 1 Electromagnetic EM Waves Antennas Key Equation c f wavelength speed of light c frequency f Antenna Efficiency Law Antenna length L a should be 2 Antennas convert electrical signals to propagating EM waves Wavelength determines antenna design and efficiency 2 Amplitude Modulation AM Core Principle Multiply the information signal by a high frequency carrier signal Modulation Equation x t A x m t c t x t Modulated signal m t Message
View Full Document