ELT 100 SURVEY OF ELECTRONICS

ELT 100 SURVEY OF ELECTRONICS

CHAPTER 41

DIGITAL FUNDAMENTALS

An extremely important chapter! Whether you want to become an electronics technician or a network administrator, the knowledge about digital circuits and the mathematics needed to analyze these circuits will be very valuable to you.

Digital systems are widespread now days. From computers and robots to microwave ovens and automobiles, they all make use of digital systems.

Digital circuits operate using only two-state signals, represented within the circuitry as two different levels of voltage. These levels of voltage are represented using different notations, for example: Low and High, L and H, On and Off, and the numbers 0 and 1. Remember, the actual values of voltages are not 0 and 1, these are only the representations used.

BINARY NUMBER SYSTEM

Because only two states are used in digital systems, binary numbers are used to analyze digital systems. The binary number system is a code system that uses only two numbers, 0 and 1, to represent any decimal number, letters of the alphabet, and any other kind of information.

The following table illustrates the representation of decimal numbers 1 through 15 using the binary system. Notice that only 0's and 1's are used. Can you see a pattern? What is number 16 in the binary system? and 19 in binary? The table below, shows two ways to represent a binary number.

Count	Decimal Number	Binary Number
Zero	0	0 or 0000
One	1	1 or 0001
Two	2	10 or 0010
Three	3	11 or 0011
Four	4	100 or 0100
Five	5	101 or 0101
Six	6	110 or 0110
Seven	7	111 or 0111
Eight	8	1000 or 1000
Nine	9	1001 or 1001
Ten	10	1010 or 1010
Eleven	11	1011 or 1011
Twelve	12	1100 or 1100
Thirteen	13	1101 or 1101
Fourteen	14	1110 or 1110
Fifteen	15	1111 or 1111

LOGIC GATES

Logic gates are devices that produce a particular output only when certain required input conditions exist. For example, a particular car may have a logic gate that will allow the starting of the car when the following input conditions are met: A key in the ignition in the on position, and automatic transmission in park. The logic gate utilized for this particular function is called an 'AND gate'. The output of this gate will be 1 (car turns ON) if and only if the two inputs are 1's at the same time: key in the ignition in the ON position (1), AND transmission in park (1). If any of these two conditions are not met, the car will not start.

Logic gates use truth tables to show the results of all possible input combinations. Since the previous example uses an AND gate, the truth table of the AND gate is shown next:

INPUTS TO THE 'AND' LOGIC GATE		OUTPUT
Key in ON position	Transmission in Park	Car Engine Condition
NO	NO	OFF
NO	YES	OFF
YES	NO	OFF
YES	YES	ON

The general form of the truth table of an AND gate with only two inputs is represented as:

INPUTS		OUTPUT
X	Y	Z
0	0	0
0	1	0
1	0	0
1	1	1

Can you see the similarities between these previous two tables?

Here is an example of a car system that uses a different type of logic gate. The engine light of the car in our discussion will light up if either of these two conditions exist: 1) the engine oil level is low, OR 2) the transmission oil level is low. Notice than in this case, any single situation, or input 1, is enough to cause the engine light to turn on, output 1. The logic gate used in this system is called OR gate. Here is the truth table for this system that uses to OR gate.

INPUTS TO THE 'OR' LOGIC GATE		OUTPUT
Engine Oil Low	Transmission Oil Low	Engine Light Condition
NO	NO	OFF
NO	YES	ON
YES	NO	ON
YES	YES	ON

Using the previous table, can you write the general form of the truth table of an OR gate with only two inputs?

Another simpler gate that is very common is called the NOT gate. The NOT gate has always only one input, and just like all the other gates, only one output. The truth table of the NOT gate is illustrated next:

INPUT	OUTPUT
X	Z
0	1
1	0

Notice that the output of the NOT gate is always the inverse of the input. Because of this, the NOT gate is also called inverter gate.

Other gates that you need to study, understand, and memorize their truth table are: the NAND gate, the NOR gate, and the X-OR gate (exclusive OR).

IMPORTANT NOTES

This is another long chapter, in this case you do not need to read the entire chapter. Read only the first five sections. Sections 4 and 5 are of particular importance. Study them hard!

NOTES FOR SELF EVALUATION

Answer Review Questions 1 through 20. Solve Problem 4. Perform Critical Thinking problems 1, 2, and 3.

Take the Practice Quiz for Chapter 41.

NOT ENOUGH?

Actually you probably are having enough material to keep you very busy. In any case, here are some links you may want to check out

Micron Electronics

http://www.micron.com/

U S Digital

http://www.usdigital.com/

Compaq

http://www.compaq.com/