Tutorials

Digital Logic Design
Basics

SPEEDING TECHNOLOGY: TODAY’S TOMORROW

From now, we’ll study how a modern processor is built starting with basic logic elements as building blocks.  Why study logic design?

• Understand what processors can do fast and what they can’t do fast (avoid slow things if you want your code to run fast!)
• Background for more detailed hardware courses

As computer Science Students, its necessary to have an idea on digital logic and design
because the language the computer understands is 0/1, on/off, or high/low in its transmission.

The headache of the computer engineer is to design a system that is small: not bulky like the
incredible hulk, fast with a high performance and considerably less expensive in the area of circuitry.
I could remember my first laptop: a Pentium II.Slower than the world Wide Web literally, it was bulky enough to be used in the olympic sports of weights.

With much to the understanding of binary computations [0 and 1]: Binary Multiplexor, Binary Adder, Binary Subtractor are some basic computations.

In Basic Electronics, there is the use of digital logic and design

From 0 volts –> 3  volts      —Voltage Level 0
From 3 volts –> .. volts     —Voltage Level 1

Logic Gates

The five Basic Gates

Boolean Algebra

How to simplify Boolean expression?

Using just ‘0’ and ‘1’s (after George Boole) Truth Table.  A Boolean function with n variables has only 2^n possible input combinations. A table with 2^n rows

Trial Example 1.0:

Draw the logic tables, Timing diagram and logic gate for the expression below. Simplify where possible.

X (Z+ Z’) + (XYZ) + (X’YZ) + (XZ)

• Am trying my possible best to explain or perhaps use terms my little kid sister would understand. She is a computer geek; more like me.

The logic table for the above example would look very much like this:

Within the logic table are 0/1, so my apologies for the images.  A look at the expression indicates that there are three principal outputs: X,Y,Z. From our initial tutorial, we could determine the number of needed rows to be N=2^3 = 8. That is how come we have three rows.

This is the way your timing diagram should look as in the above:

This is the logic gate.