Introduction to Combinational Logic

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Course Objectives[edit]

This course will present the student with basic concepts and methods of analysis as it is applied to combinational circuits. This course assumes student has fundamental knowledge of basic circuit analysis (Ohm's Law, Node Voltage, Mesh Current, Norton, Thevenin, and Superposition).

Number Systems and Conversions[edit]

Basic Ideas and Concepts[edit]

  • The idea of a digit and what the digit can represent and its application to different numerical systems
  • How to determine an equivalent numerical representation in a different numerical system
  • How to add and subtract binary numbers
  • Understand the differences between signed and unsigned numbers
  • Understand how to represent signed numbers in binary
  • How to determine the one’s and two’s complement of a binary number

Numerical Systems[edit]

We will cover the four basic numerical systems (decimal, binary, octal, and hexadecimal) and determine the conversions between each of them. A numerical system is in a simple sense, another way to represent a value of something.

Signed and Unsigned Numbers[edit]

We can easily represent positive or unsigned numbers in any numerical system we wish, however, when a number is not positive, we introduce the concept of signed numbers. In the binary system, there are three ways to represent a signed number: sign and magnitude, one’s complement, and two’s complement.

Digitization, Logic Gates, and Symbols[edit]

Basic Ideas and Concepts[edit]

  • Learn what is referred to as a "digital" circuit
  • Learn the respective logic gates and symbols associated
  • Learn the functionality of each logic gate

Truth Tables and Boolean Algebra[edit]

Basic Ideas and Concepts[edit]

  • What is a truth table and what can it do
  • Mapping a function on a truth table and determining all possible outputs
  • Applying principles of Boolean Algebra to minimize given function
  • Learn how to apply minterms and maxterms expansion to a truth table

Formulate a truth table for the given function below:

Minimization and Implementation with Karnaugh Maps[edit]

Adders, Subtracters, Multipliers, and Comparators[edit]

(001010) + (110101)

Multiplexers, Encoders, and Decoders[edit]

Programmable Logic Devices and HDLs[edit]

References and Contributors[edit]

Textbook used: Fundamentals of Digital Logic by Brown and Vranesic Copyright 2003, McGraw Hill Higher-Ed

Vincent Nhieu, Student
California State Polytechnic University, Pomona