Discrete Mathematics

  1. Boolean Algebra and Logic Circuits
    1. Boolean Algebra Fundamentals
      1. Boolean Variables and Functions
        1. Binary Variables
          1. Boolean Operations
            1. Truth Tables for Boolean Functions
            2. Boolean Laws and Identities
              1. Commutative Laws
                1. Associative Laws
                  1. Distributive Laws
                    1. Identity Laws
                      1. Complement Laws
                        1. Absorption Laws
                          1. De Morgan's Laws
                          2. Boolean Function Representation
                            1. Sum of Products Form
                              1. Product of Sums Form
                                1. Canonical Forms
                                  1. Minterms and Maxterms
                                2. Logic Gates and Circuits
                                  1. Basic Logic Gates
                                    1. AND Gate
                                      1. OR Gate
                                        1. NOT Gate
                                          1. NAND Gate
                                            1. NOR Gate
                                              1. XOR Gate
                                              2. Gate Combinations
                                                1. Compound Gates
                                                  1. Universal Gates
                                                    1. Gate Equivalences
                                                    2. Circuit Design
                                                      1. From Boolean Expressions
                                                        1. From Truth Tables
                                                          1. Multi-Level Circuits
                                                        2. Boolean Function Minimization
                                                          1. Algebraic Minimization
                                                            1. Using Boolean Laws
                                                              1. Factoring and Expansion
                                                                1. Systematic Approaches
                                                                2. Karnaugh Maps
                                                                  1. Construction of K-Maps
                                                                    1. Grouping Rules
                                                                      1. Minimization Process
                                                                        1. Don't Care Conditions
                                                                        2. Quine-McCluskey Method
                                                                          1. Tabular Minimization
                                                                            1. Prime Implicants
                                                                              1. Essential Prime Implicants
                                                                            2. Applications in Digital Systems
                                                                              1. Combinational Circuits
                                                                                1. Adders
                                                                                  1. Multiplexers
                                                                                    1. Decoders
                                                                                      1. Encoders
                                                                                      2. Sequential Circuits
                                                                                        1. Flip-Flops
                                                                                          1. Counters
                                                                                            1. Registers
                                                                                            2. Computer Arithmetic
                                                                                              1. Binary Addition
                                                                                                1. Binary Subtraction
                                                                                                  1. Overflow Detection

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                                                                                              8. Algorithms and Complexity

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                                                                                              1. Foundations of Logic and Proofs