Experiments with Digital Systems.

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Abstract:

        The Lab, Experiments with Digital Systems, gave us a chance to get some hands on experience with simple logic circuits, and see them work.  This lab also introduced us to the Laws of Boolean Algebra.  We also saw how a computer can interact with a circuit outside of the computer.

Introduction:

        A digital system is a combination of circuits connected in some specific way to perform a specified function where all variables involved are allowed only a finite number of discrete states or values.  The values that the circuit understands are in a form called binary.  Binary signals consist of two numbers 0 and 1.  A one represents the presence of voltage, a zero, on the other hand, represents the absence of voltage.  Zeros and ones can also represent on/off, true/false, etc.  The combinations of these 0’s and 1’s are used to represent numbers, characters, and other information.  There are certain rules and theorems that make up the fundamental concepts of a binary system.  These fundamental concepts are known as Boolean algebra.  Boolean algebra is vital because its applications directly lead to techniques that are essential in designing efficient digital systems.  An x-bit binary system is capable of 2x combinations/values.  For example, an eight-bit system is capable of 28 or 256 combinations/values.  However, since you begin with the number 0 we can only represent up to the number 255.  This lab only involves 1-bit numbers.

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Boolean algebra has three basic logic functions and 3 derived logic functions.  The basic logic functions are: AND, OR, and NOT.  The three derived logic functions are: NAND, NOR, and XOR.  In this lab we will just be manipulating 2-4 one-bit inputs: A, B, C, and D.  Each logic function will compare these inputs and spit out a value based one the inputs.  The AND function will output the value of A and B if they are the same value or it will output a 0 if A is different from B.  The NAND function will see the inputs as ...

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