Foundations of Digital Design

The outlined road map for most students in EE at UMD (they change it every now and then: can be found here) has digital logic, ENEE244, covered before basic circuit theory. I agree with this layout as digital circuits are extremely easy to understand fundamentally and then provide the motivation to conquer analog circuits.

The textbook for this course, which is 100% needed, is Digital Principles and Design with CD-ROM It can be found pretty cheap used on amazon, whereas the bookstore on campus sells it new for $193.00 (rip off).

Regardless of who teaches this course, Silio or Nakajima, this book will be your number one source of learning.



Note: Both professors have terrible reviews (see ourumd.com for reviews), but both follow very similar exam format and questions. The class really isn't that bad as long as you put forth some effort.

If you wish to pursue computer engineering or anything digital related, this class is an extremely important foundation. It is also in my opinion the last "weed" out course for the degree program.



I cant recommend the book any more than already stated, and will demonstrate some of the harder problems found within the text here.

However this is a great website in order to get an almost textbook in depth explanation of Boolean Algebra: Art of Assembly

Another textbook that builds off of the required text and expands in to more computer design is:  Digital Design and Computer Architecture

Boolean Algebra

Boolean Algebra is the math of logic essentially. It was developed by George Boole as a way of mathematically representing relays in telephone systems in 1938 by Claude E. Shannon (everybody should read a bio on him!)

This algebra has been used ever since to represent combinational and sequential networks. The nuts and bolts are very simple:

Lets say there is a value 'X', then X OR X' = 1, X AND X' = 0

This sentence essentially contains all the postulates the describe the algebra. something or its inverse (represented here by the ') will be 0. That is due to the fact that if X is 0, than its inverse, X' is 1. So X+X' =1

note: from now on + will be the or function, and * will be the and function

There are a total of 6 postulates that describe the algebra and are found on page 62 of the textbook. I will not cover them here as the book does a great job, and through the examples you should be able to pick up on them as they are fundamentally simple and used to prove many theorems throughout the book.

Lets do two problems that sum up boolean algebra:

1.  Prove xy + xy' +x'y' = x + y'
1. regroup as: x( y + y') + x'y' = x + y'
2. recall from above that y + y' = 1, so x*1 + x'y' = x + y'
3. x*1 => x, now we have x + x'y' = x + y'
4. we can simplify this by use of a Theorem 3.7 on page 67 x + x'y = x + y
5. we are left with x + y' = x + y'

     2.   Prove xy + yz + x'z = xy +x'z
               1.  this requires expansion of the yz term so yz*1, yz(x+x')
               2.  this gives us xy + yzx + yzx' + x'z = xy + x'z
               3.  rearrange as xy(z+1) + x'z(y+1) = xy + x'z
               4.  recall any element or'ed with 1 = 1; so we get xy*1 + x'z*1 = xy + x'z
               5.  recall any element and'ed with 1 = itself, so we end up with xy + x'z



This is by no means (and obviously) an exhaustive study guide for boolean algebra, but it does serve as an indicator on what to expect when dealing with these problems.


Quick note for those who will take ENEE244 at UMD

Make sure that you do not skip a single step, leave out an '=', or forget to label which postulate or theorem you used in order to solve that step. Nakajima will take all the points away if you do that on an exam!!

I might post my old exams as well as the solutions to them if I can find them

If you have any questions about boolean algebra please leave it as a comment for all to see.

-Brian