Digital Logic Design

Digital Logic Design is a fundamental discipline within computer engineering that deals with the design and implementation of circuits that operate on discrete binary values, typically represented as 0s and 1s. It applies the principles of Boolean algebra to create elementary building blocks called logic gates (such as AND, OR, and NOT), which are then combined into more complex combinational and sequential circuits like adders, multiplexers, and memory elements. This field provides the essential hardware foundation upon which all modern digital systems are built, including microprocessors, memory, and the vast array of electronic devices that define our technological world.

1. Foundations of Digital Logic
   1. Digital vs. Analog Systems
      1. Definition of Digital Systems
      2. Definition of Analog Systems
      3. Continuous vs. Discrete Signals
         1. Characteristics of Continuous Signals
         2. Characteristics of Discrete Signals
      4. Advantages of Digital Systems
         1. Noise Immunity
         2. Ease of Storage and Processing
         3. Reproducibility and Reliability
         4. Scalability and Flexibility
      5. Applications of Digital Systems
   2. Number Systems
      1. Positional Number Systems
         1. Concept of Place Value
         2. Base or Radix Definition
      2. Binary Number System
         1. Representation of Numbers
         2. Counting in Binary
         3. Binary Weights
      3. Octal Number System
         1. Representation of Numbers
         2. Counting in Octal
      4. Decimal Number System
         1. Representation of Numbers
         2. Counting in Decimal
      5. Hexadecimal Number System
         1. Representation of Numbers
         2. Counting in Hexadecimal
         3. Hexadecimal Digits
      6. Number Base Conversions
         1. Any Base to Decimal
            1. Integer Conversion
            2. Fractional Conversion
         2. Decimal to Any Base
            1. Integer Conversion
            2. Fractional Conversion
         3. Binary to Octal Conversion
         4. Binary to Hexadecimal Conversion
         5. Octal to Binary Conversion
         6. Hexadecimal to Binary Conversion
         7. Direct Conversion Methods
   3. Binary Arithmetic
      1. Binary Addition
         1. Rules of Binary Addition
         2. Carry Generation
         3. Multi-bit Addition
      2. Binary Subtraction
         1. Rules of Binary Subtraction
         2. Borrowing in Binary
         3. Multi-bit Subtraction
      3. Binary Multiplication
         1. Rules of Binary Multiplication
         2. Partial Products
         3. Shift and Add Method
      4. Binary Division
         1. Rules of Binary Division
         2. Remainder and Quotient
         3. Long Division Method
   4. Representation of Negative Numbers
      1. Signed-Magnitude Representation
         1. Format and Range
         2. Limitations
         3. Arithmetic Operations
      2. 1's Complement Representation
         1. Formation of 1's Complement
         2. Range and Properties
         3. Arithmetic Operations
      3. 2's Complement Representation
         1. Formation of 2's Complement
         2. Range and Properties
         3. Advantages over Other Methods
      4. 2's Complement Arithmetic
         1. Addition and Subtraction
         2. Overflow Detection
         3. Sign Extension
   5. Binary Codes
      1. Binary Coded Decimal
         1. BCD Representation
         2. BCD Addition
         3. Excess-3 Code
      2. Gray Code
         1. Generation of Gray Code
         2. Binary to Gray Conversion
         3. Gray to Binary Conversion
         4. Applications of Gray Code
      3. ASCII Code
         1. Structure of ASCII
         2. Character Encoding
         3. Extended ASCII
      4. Error Detecting and Correcting Codes
         1. Parity Bits
            1. Even Parity
            2. Odd Parity
            3. Parity Error Detection
            4. Limitations of Parity
         2. Hamming Code
            1. Hamming Distance
            2. Error Detection and Correction Capability
            3. Encoding Process
            4. Decoding Process
            5. Single Error Correction Double Error Detection