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Introduction - Why Do You Want to Learn This Material?

        In this lesson you're going to be introduced to Digital Logic.  There are lots of reasons to learn digital logic.  Here are some of those reasons.

  • Digital logic is the foundation for digital computers.  If you want to understand the innards of computers you need to know digital logic.

  • Digital logic has relations to other kinds of logic including:

    • Formal logic - as taught by many philosophy departments

    • Fuzzy logic - a tool used to design control systems and many other systems.

    • So, in learning digital logic you learn something that helps you elsewhere.

  • For many students, learning digital logic is fun.

What Are You Going to Learn?

        There are at least two general areas you need to become familiar with.

  • First, there's background you need to know - the basics of digital logic - things like zeros and ones (0s and 1s) and how you can represent signals as sequences of zeroes and ones.  Eventually you will want to know how large arrays of zeroes and ones can be used in computer files to store information in pictures, documents, sounds and even movies and you'll want to learn about how information can be transmitted, between computers and digital signal sources.

  • You will also need to know things about digital circuits - gates, flip-flops and memory elements and others - so that you can eventually design circuits to manipulate digital signals.

Here is a short list of the topics you will learn.

  • Learn what logic signals look like

  • Model logic signals

  • Learn Boolean algebra for logic analysis

  • Learn about gates that process logic signals

  • Learn how to design some smaller logic circuits

  • Learn about flip-flops and memory elements that store logic signals

Objectives For This Lesson

 Here's what we are after in this lesson - what you should be able to do.

   Given a system that uses logic signals

   Be able to specify what the output will be when the input is zero (0) and what  the output will be when the input is one (1).

   Given an AND, OR, NAND or NOT gate,

   Be able to determine the output of the gate given the input logic signals.

   Given a system that requires gates,

Be able to wire a chip correctly, and to  check that the chip is functioning properly.

Logic Signals

        There are a number of different systems for representing binary information in physical systems.  Here are a few.

  • A voltage signal with zero (0) corresponding to 0 volts and one (1) corresponding to five or three volts.

  • A sinusoidal signal with zero corresponding to some frequency, and one corresponding to some other frequency.

  • A current signal with zero corresponding to 4 milliamps and one corresponding to 20 milliamps.

  • And one last way is to use switches, OPEN for "0" and CLOSED for "1".

  • (And there are more ways!)

Characteristics of Logic Signals

        We should note that all of these signals can and usually will change in time, so that we really are looking at dynamic situations.  However, we will start by looking at these signals as though they were not changing in time.

  • We will pick a voltage signal as a working example.  It can take on two values corresponding to 0 and 1.

  • We can associate a variable with that logic signal, and we can assign a symbol to represent that variable - like the symbol A.

Think Binary!

        Let's examine a typical situation.  You have some sort of device that generates a logic signal.

  • It could be a telephone that converts your voice signal into a sequence of zeros and ones.

  • It could be the thermostat on the wall that generates a 1 when the temperature is too low, and a 0 when the temperature is above the set point temperature.

        The logic signal, A, takes on values of 0 (FALSE, OFF) or 1 (TRUE, ON).  That signal might really be a voltage, a switch closure, etc.  However, we want to think in terms of zeros and ones, not in terms of the values of the voltage.

Operations on Logic Signals

        Once we have the concept of a logic signal we can talk about operations that can be performed on logic signals.  Begin by assuming we have two logic signals, A and B.  Then assume that those two signals form an input set to some circuit that takes two logic signals as inputs, and has an output that is also a logic signal.  That situation is represented below.

        The output, C, depends upon the inputs, A and B.  There are many different ways that C could depend upon A and B.  The output, C, is a function, - a logic function - of the inputs, A and B.  IWe will examine a few basic logic functions - AND, OR and NOT functions and start learning the circuitry that you use to implement those functions. 

Logic Gates

        If we think of two signals, A and B, as representing a truth value of two different propositions, then A could be either TRUE (a logical 1) or FALSE (a logical 0).  B can take on the same values.  Now consider a situation in which the output, C, is TRUE only when both A is TRUE and B is TRUE.  We can construct a truth table for this situation. In that truth table, we insert all of the possible combinations of inputs, A and B, and for every combination of A and B we list the output, C.
















An AND Example

        Let's imagine a physician prescribing two drugs.  For some conditions drug A is prescribed, and for other conditions drug B is prescribed.  Taken separately each drug is safe.  When used together dangerous side effects are produced.


  • A = Truth of the statement "Drug 'A' is prescribed.".

  • B = Truth of the statement "Drug 'B' is prescribed.".

  • C = Truth of the statement "The patient is in danger.".

Then, the truth table below shows when the patient is in danger.
















Notice that C is TRUE when both A AND B are true and only then!


        An AND function can be implemented electrically using a device known as an AND gate.  You might imagine a system in which zero (0) is represented by zero (0) volts, and one (1) is represented by three (3) volts, for example.  If we are going to use electrical devices we need some sort of symbolic representation.  There is a standard symbol for an AND gate shown below.

        Often in lab work it's helpful to use an LED to show when a signal is 0 or 1.  Usually a 1 is indicated with an LED that is ON (i.e. glowing).  You can use the buttons below to check out this AND gate (Note what an AND gate symbol looks like!) with a simulated LED.  Note the following in the simulation (and you can use this in your lab experiments).


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