1. Scientific & Engineering Notation
Digital Electronics TM
1.1 Foundations and The Board Game Counter
2013 Final Exam Study Guide
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Copyright 2009

2. What is a resistor?
What are capacitors?
What is the difference from an analog and digital signal?
What is a truth table?
Properly construct a truth table.
Write a Sum-Of-Products (SOP) logic expression from a truth table.
Create a truth table given a SOP logic expression.
Mathematically express the relationship between the number of input (N) and the number of input combinations.
Find simplified SOP logic expression.
What is a don’t care condition?
What is a Nand gate?
What is a NOR gate?

3. Scientific & Engineering Notation
Digital Electronics TM
1.1 Foundations and The Board Game Counter
Scientific & Engineering Notation
This presentation will demonstrate…
How to express numbers in scientific notation.
How to express numbers in engineering notation.
How to express numbers in SI prefix notation.
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Copyright 2009

4. Scientific & Engineering Notation
Digital Electronics TM
1.1 Foundations and The Board Game Counter
Scientific Notation
Scientific notation is a way of writing very large and very small numbers in a compact form.
A number written in scientific notation is written in the form:
a × 10b
Where: a is a number greater than 1 and less than 9.99
b is an integer
Examples:
3.24 × 105
1.435 × 10-7
3.29× 106
7.3 × 10−2
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5. Scientific Notation: Example #1
Scientific & Engineering Notation
Digital Electronics TM
1.1 Foundations and The Board Game Counter
Scientific Notation: Example #1
Example:
Express 5630 in scientific notation. 5
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6. Scientific Notation: Example #2
Scientific & Engineering Notation
Digital Electronics TM
1.1 Foundations and The Board Game Counter
Scientific Notation: Example #2
Example:
Express in scientific notation. 6
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7. Scientific & Engineering Notation
Digital Electronics TM
1.1 Foundations and The Board Game Counter
Engineering Notation
Engineering notation is similar to scientific notation. In engineering notation the powers of ten are always multiples of 3.
A number written in engineering notation is written in the form:
a × 10b
Where: a is a number greater than 1 and less than 999
b is an integer multiple of three
Examples:
71.24 × 103
4.32 × 10-6
320.49× 109
× 10−12
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8. Writing A Number in Engineering Notation
Scientific & Engineering Notation
Digital Electronics TM
1.1 Foundations and The Board Game Counter
Writing A Number in Engineering Notation
Shift the decimal point in “groups of three” until the number before the decimal point is between 0 and 999.
Multiply by a power of 10 that is equal to the number of places the decimal point has been moved.
The power of 10 is positive if the decimal point is moved to the left and negative if the decimal point is moved to the right.
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9. Engineering Notation: Example #1
Scientific & Engineering Notation
Digital Electronics TM
1.1 Foundations and The Board Game Counter
Engineering Notation: Example #1
Example:
Express in engineering notation. 9
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10. Engineering Notation: Example #2
Scientific & Engineering Notation
Digital Electronics TM
1.1 Foundations and The Board Game Counter
Engineering Notation: Example #2
Example:
Express in engineering notation. 10
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11. Scientific & Engineering Notation
Digital Electronics TM
1.1 Foundations and The Board Game Counter
SI Prefixes
SI prefixes are a shorthand way of writing engineering notation for SI numbers.
The International System of Units (abbreviated SI from the French Système International d'Unités) is the modern form of the metric system. It is the world's most widely used system of units for science and engineering.
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12. Commonly Used SI Prefixes
Scientific & Engineering Notation
Digital Electronics TM
1.1 Foundations and The Board Game Counter
Commonly Used SI Prefixes
Value
Prefix
Symbol
1012
tera T
109
giga G
106
mega M
103
kilo k
10-3
milli m
10-6
micro 
10-9
nano n
10-12
pico p
10-15
femto f
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13. Scientific & Engineering Notation
Digital Electronics TM
1.1 Foundations and The Board Game Counter
SI Notation: Example #1
Example:
Express  using standard SI notation.
(Note:  is the Greek letter omega. In electronics, it is the symbol used for resistance.) 13
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14. Scientific & Engineering Notation
Digital Electronics TM
1.1 Foundations and The Board Game Counter
SI Notation: Example #2
Example:
Express Volts using standard SI notation. 14
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15. Common Electronic Symbol & Units
Scientific & Engineering Notation
Digital Electronics TM
1.1 Foundations and The Board Game Counter
Common Electronic Symbol & Units
Quantity
Symbol
Unit
Current I
Ampere (A)
Voltage V
Volt (V)
Resistance R
Ohm ()
Frequency f
Hertz (Hz)
Capacitance C
Farad (F)
Inductance L
Henry (H)
Power P
Watt (W)
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16. Component Identification
Digital Electronics TM
1.1 Foundations and The Board Game Counter
Resistors
A resistor is an electronic component that resists the flow of electrical current.
A resistor is typically used to control the amount of current that is flowing in a circuit.
Resistance is measured in units of ohms () and named after George Ohm, whose law (Ohm’s Law) defines the fundamental relationship between voltage, current, and resistance.
Definition of a Resistor.
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17. How To Read A Resistor’s Value
Component Identification
Digital Electronics TM
1.1 Foundations and The Board Game Counter
How To Read A Resistor’s Value
Resistor Color Code
Resistor color code chart.
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18. Resistor Value: Example #1
Component Identification
Digital Electronics TM
1.1 Foundations and The Board Game Counter
Resistor Value: Example #1
Example:
Determine the nominal value for the resistor shown.
Pause the presentation and allow students to complete the example. The solution is on the next slide.
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19. Resistor Value: Example #1
Component Identification
Digital Electronics TM
1.1 Foundations and The Board Game Counter
Resistor Value: Example #1
Example:
Determine the nominal value for the resistor shown.
Solution:
10 x 100  5%
1000  5%
1 K  5%
This slide includes the solution to Resistor Value Example #1. If you print handouts, do not print this page.
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20. Resistor Value: Example #3
Component Identification
Digital Electronics TM
1.1 Foundations and The Board Game Counter
Resistor Value: Example #3
Example:
Determine the color bands for a 1.5 K  5% resistor. ? ? ? ?
Pause the presentation and allow students to complete the example. The solution is on the next slide.
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21. Resistor Value: Example #3
Component Identification
Digital Electronics TM
1.1 Foundations and The Board Game Counter
Resistor Value: Example #3
Example:
Determine the color bands for a 1.5 K  5% resistor. ? ? ? ?
Solution:
1.5 K  5%
1500  5%
15 x 100  5%
1: Brown
5: Green
100: Red
5%: Gold
This slide includes the solution to Resistor Value Example #3. If you print handouts, do not print this page.
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22. Component Identification
Digital Electronics TM
1.1 Foundations and The Board Game Counter
Capacitors
A capacitor is an electronic component that can be used to store an electrical charge.
Capacitors are often used in electronic circuits as temporary energy-storage devices.
Capacitance is measured in units of farads (F) and named after Michael Faraday, a British chemist and physicist who contributed significantly to the study of electromagnetism.
Definition of a Capacitor.
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23. How To Read A Capacitor’s Value
Component Identification
Digital Electronics TM
1.1 Foundations and The Board Game Counter
How To Read A Capacitor’s Value
Disc Capacitors
Code
Tolerance A
±0.05% B
±0.1% C
±0.25% D
±0.5% F
±1% G
±2% J
±5% K
±10%
M or NONE
±20% N
±30% Q
−10%, +30% S
−20%, +50% T
−10%, +50% Z
−20%, +80% 4 7 2 K
First Digit
First Figure
Second Digit
Second Figure
Third Digit
# of Zeros
Fourth Digit
Tolerance
Overview of how a disc capacitor is labeled. 4 7 00 K
4700 pF 10%
Note: Units on Disc Capacitors are always in pico-farads
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24. Component Identification
Digital Electronics TM
1.1 Foundations and The Board Game Counter
Capacitor: Example #1
Example:
Determine the nominal value for the capacitor shown.
Code
Tolerance A
±0.05% B
±0.1% C
±0.25% D
±0.5% F
±1% G
±2% J
±5% K
±10%
M or NONE
±20% N
±30% Q
−10%, +30% S
−20%, +50% T
−10%, +50% Z
−20%, +80%
Pause the presentation and allow students to complete the example. The solution is on the next slide.
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25. Component Identification
Digital Electronics TM
1.1 Foundations and The Board Game Counter
Capacitor: Example #1
Example:
Determine the nominal value for the capacitor shown.
Code
Tolerance A
±0.05% B
±0.1% C
±0.25% D
±0.5% F
±1% G
±2% J
±5% K
±10%
M or NONE
±20% N
±30% Q
−10%, +30% S
−20%, +50% T
−10%, +50% Z
−20%, +80%
Solution:
330 pF 5%
This slide includes the solution to Capacitor Value Example #1. If you print handouts, do not print this page.
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26. Analog and Digital Signals
Digital Electronics TM
1.2 Introduction to Analog
Analog and Digital Signals
Analog Signals
Digital Signals
Continuous
Infinite range of values
More exact values, but more difficult to work with
Discrete
Finite range of values (2)
Not as exact as analog, but easier to work with
Example:
A digital thermostat in a room displays a temperature of 72. An analog thermometer measures the room temperature at . The analog value is continuous and more accurate, but the digital value is more than adequate for the application and significantly easier to process electronically.
This slide defines analog and digital signals and gives several examples of each.
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27. Example of Analog Signals
Analog and Digital Signals
Digital Electronics TM
1.2 Introduction to Analog
Example of Analog Signals
An analog signal can be any time-varying signal.
Minimum and maximum values can be either positive or negative.
They can be periodic (repeating) or non-periodic.
Sine waves and square waves are two common analog signals.
Note that this square wave is not a digital signal because its minimum value is negative.
0 volts
Sine Wave
Square Wave
(not digital)
Random-Periodic
Examples of common analog signals.
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28. Parts of an Analog Signal
Analog and Digital Signals
Digital Electronics TM
1.2 Introduction to Analog
Parts of an Analog Signal
Amplitude
(peak-to-peak)
(peak)
Period
(T)
Frequency:
Parts of an analog signal: amplitude, period, & frequency.
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29. Example of Digital Signals
Analog and Digital Signals
Digital Electronics TM
1.2 Introduction to Analog
Example of Digital Signals
Digital signal are commonly referred to as square waves or clock signals.
Their minimum value must be 0 volts, and their maximum value must be 5 volts.
They can be periodic (repeating) or non-periodic.
The time the signal is high (tH) can vary anywhere from 1% of the period to 99% of the period.
5 volts
Examples of common digital signals.
0 volts
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30. Parts of a Digital Signal
Analog and Digital Signals
Digital Electronics TM
1.2 Introduction to Analog
Parts of a Digital Signal
Amplitude:
For digital signals, this will ALWAYS be 5 volts.
Period (T):
The time it takes for a periodic signal to repeat. (in seconds)
Frequency (F):
A measure of the number of cycles of the signal per second. (in Hertz, Hz)
Time High (tH):
The time (in sec.) the signal is high or 5v.
Time Low (tL):
The time (sec.) the signal is low or 0v.
Duty Cycle (DC) (%):
The ratio of tH to the period (T), expressed as a percentage.
Rising Edge:
A 0-to-1 transition of the signal.
Falling Edge:
A 1-to-0 transition of the signal.
Falling Edge
Time
High
(tH)
Amplitude
Time
Low
(tL)
Rising Edge
Period (T)
The parts of a digital signal: amplitude, period & frequency, time high, time low, duty cycle, rising & falling edge.
Frequency (F):
Duty Cycle (%):
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31. Example: Digital Signal
Analog and Digital Signals
Digital Electronics TM
1.2 Introduction to Analog
Example: Digital Signal
Example:
Determine the following information for the digital signal shown:
Amplitude
Period (T)
Frequency (f)
Time High (tH)
Time Low (tL)
Duty Cycle (DC)
Pause the presentation and allow the student to work on the example. The solution is on the next two slides.
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32. Example: Digital Signal
Analog and Digital Signals
Digital Electronics TM
1.2 Introduction to Analog
Example: Digital Signal
Solution:
Amplitude:
Period (T):
Frequency (F): 4V 2V
2ms
4ms
Here is the solution. If you print handouts, do not print this page. (1 of 2)
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33. Example: Digital Signal
Analog and Digital Signals
Digital Electronics TM
1.2 Introduction to Analog
Example: Digital Signal
Solution:
Time High (tH):
Time Low (tL):
Duty Cycle (DC) %:
Here is the solution. If you print handouts, don’t print this page. (2 of 2)
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34. Decimal ‒to‒ Binary Conversion
Binary Number System
Digital Electronics
2.1 Introduction to AOI Logic
Decimal ‒to‒ Binary Conversion
The Process : Successive Division
Divide the Decimal Number by 2; the remainder is the LSB of Binary Number .
If the quotient is zero, the conversion is complete; else repeat step (a) using the quotient as the Decimal Number. The new remainder is the next most significant bit of the Binary Number.
Example:
Convert the decimal number 610 into its binary equivalent.
Review the DECIMAL-to-BINARY conversion process.
Remind the students to subscript all numbers (i.e. Subscript 10 for decimal & subscript 2 for binary)
A common mistake is inverting the LSB and MSB.
The three-dot triangular symbol here stands for the word “therefore” and is used commonly among mathematics scholars.
 610 = 1102
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35. Dec → Binary : Example #1 Example:
Binary Number System
Digital Electronics
2.1 Introduction to AOI Logic
Dec → Binary : Example #1
Example:
Convert the decimal number 2610 into its binary equivalent.
Pause the power point and allow the student to work on the example. The solution is on the next slide.
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36. Dec → Binary : Example #1 Example:
Binary Number System
Digital Electronics
2.1 Introduction to AOI Logic
Dec → Binary : Example #1
Example:
Convert the decimal number 2610 into its binary equivalent.
Solution:
 =
Here is the solution. If you print handouts, don’t print this page.
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37. Binary ‒to‒ Decimal Process
Binary Number System
Digital Electronics
2.1 Introduction to AOI Logic
Binary ‒to‒ Decimal Process
The Process : Weighted Multiplication
Multiply each bit of the Binary Number by it corresponding bit- weighting factor (i.e. Bit-0→20=1; Bit-1→21=2; Bit-2→22=4; etc).
Sum up all the products in step (a) to get the Decimal Number.
Example:
Convert the decimal number into its decimal equivalent. 1 23 22 21 20 8 4 2 + =
610
Review the BINARY-to-DECIMAL conversion process.
Remind the students to subscript all numbers (i.e. Subscript 10 for decimal & subscript 2 for decimal)
Let the students know that as the become more proficient at the conversions, they may not need to write out the Bit-Weighting Factors.
 = 6 10
Bit-Weighting
Factors
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38. Binary → Dec : Example #1 Example:
Binary Number System
Digital Electronics
2.1 Introduction to AOI Logic
Binary → Dec : Example #1
Example:
Convert the binary number into its decimal equivalent.
Pause the power point and allow the student to work on the example. The solution is on the next slide.
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39. Base10 Base2 Base10 Base2 Summary & Review DECIMAL BINARY DECIMAL
Binary Number System
Digital Electronics
2.1 Introduction to AOI Logic
Summary & Review
Base10
DECIMAL
Base2
BINARY
Successive
Division
Divide the Decimal Number by 2; the remainder is the LSB of Binary Number .
If the Quotient Zero, the conversion is complete; else repeat step (a) using the Quotient as the Decimal Number. The new remainder is the next most significant bit of the Binary Number.
Weighted
Multiplication
Base10
DECIMAL
Base2
BINARY
Prior to assigning the activity, review the process for DECIMAL-to-BINARY and BINARY-to-DECIMAL.
Multiply each bit of the Binary Number by it corresponding bit-weighting factor (i.e. Bit-0→20=1; Bit-1→21=2; Bit-2→22=4; etc).
Sum up all the products in step (a) to get the Decimal Number.
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40. Karnaugh Mapping
Digital Electronics
2.2 Intro to NAND & NOR Logic
K-Map Format
Each minterm in a truth table corresponds to a cell in the K-Map.
K-Map cells are labeled such that both horizontal and vertical movement differ only by one variable.
Since the adjacent cells differ by only one variable, they can be grouped to create simpler terms in the sum-of- products expression.
The sum-of-products expression for the logic function can be obtained by OR-ing together the cells or group of cells that contain 1s.
Explain how a K-Map is formatted and how a simplified logic expression can be written from the cell groupings.
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41. K-Map Simplification Process
Karnaugh Mapping
Digital Electronics
2.2 Intro to NAND & NOR Logic
K-Map Simplification Process
Construct a label for the K-Map. Place 1s in cells corresponding to the 1s in the truth table. Place 0s in the other cells.
Identify and group all isolated 1’s. Isolated 1’s are ones that cannot be grouped with any other one, or can only be grouped with one other adjacent one.
Group any hex.
Group any octet, even if it contains some 1s already grouped but not enclosed in a hex.
Group any quad, even if it contains some 1s already grouped but not enclosed in a hex or octet.
Group any pair, even if it contains some 1s already grouped but not enclosed in a hex, octet, or quad.
OR together all terms to generate the SOP equation.
Steps for simplifying using the K-Map process.
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42. Example #1: 2 Variable K-Map
Karnaugh Mapping
Digital Electronics
2.2 Intro to NAND & NOR Logic
Example #1: 2 Variable K-Map
Example:
After labeling and transferring the truth table data into the K-Map, write the simplified sum-of-products (SOP) logic expression for the logic function F1. V J K F1 1
Pause the presentation and allow the student to complete the example. The solution is on the next slide.
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43. Example #1: 2 Variable K-Map
Karnaugh Mapping
Digital Electronics
2.2 Intro to NAND & NOR Logic
Example #1: 2 Variable K-Map
Example:
After labeling and transferring the truth table data into the K-Map, write the simplified sum-of-products (SOP) logic expression for the logic function F1.
Solution: V 1 J K F1 1
Here is the solution. If you print handouts, do not print this page.
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44. Example #2: 3 Variable K-Map
Karnaugh Mapping
Digital Electronics
2.2 Intro to NAND & NOR Logic
Example #2: 3 Variable K-Map
Example:
After labeling and transferring the truth table data into the K-Map, write the simplified sum-of-products (SOP) logic expression for the logic function F2. E F G F2 1
Pause the presentation and allow students to complete the example. The solution is on the next slide.
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45. Example #2: 3 Variable K-Map
Karnaugh Mapping
Digital Electronics
2.2 Intro to NAND & NOR Logic
Example #2: 3 Variable K-Map
Example:
After labeling and transferring the truth table data into the K-Map, write the simplified sum-of-products (SOP) logic expression for the logic function F2.
Solution: V 1 E F G F2 1
Here is the solution. If you print handouts, do not print this page.
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46. Truth Table to K-Map Mapping
Karnaugh Mapping
Digital Electronics
2.2 Intro to NAND & NOR Logic
Truth Table to K-Map Mapping
Four Variable K-Map W X Y Z
FWXYZ
Minterm – 0
Minterm – 1 1
Minterm – 2
Minterm – 3
Minterm – 4
Minterm – 5
Minterm – 6
Minterm – 7
Minterm – 8
Minterm – 9
Minterm – 10
Minterm – 11
Minterm – 12
Minterm – 13
Minterm – 14
Minterm – 15
Only one variable changes for every column change 1 V 1 3 2 4 5 7 6 12 13 15 14 8 9 11 10 1
Only one
variable changes
for every row
change
Demonstrate how the minterms of a four variable truth table are mapped to a K-Map. 1 1
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47. Karnaugh Mapping
Digital Electronics
2.2 Intro to NAND & NOR Logic
Don’t Care Conditions
A don’t care condition, marked by (X) in the truth table, indicates a condition where the design doesn’t care if the output is a (0) or a (1).
A don’t care condition can be treated as a (0) or a (1) in a K-Map.
Treating a don’t care as a (0) means that you do not need to group it.
Treating a don’t care as a (1) allows you to make a grouping larger, resulting in a simpler term in the SOP equation.
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48. Some You Group, Some You Don’t
Karnaugh Mapping
Digital Electronics
2.2 Intro to NAND & NOR Logic
Some You Group, Some You Don’t
This don’t care condition was treated as a (1). This allowed the grouping of a single one to become a grouping of two, resulting in a simpler term. V X 1
Explain that you include don’t care conditions only if it allows you to make a grouping larger.
There was no advantage in treating this don’t care condition as a (1), thus it was treated as a (0) and not grouped.
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49. Universal Gate – NAND This presentation will demonstrate
Digital Electronics
2.2 Intro to NAND & NOR Logic
Universal Gate – NAND
This presentation will demonstrate
The basic function of the NAND gate.
How a NAND gate can be used to replace an AND gate, an OR gate, or an INVERTER gate.
How a logic circuit implemented with AOI logic gates can be re-implemented using only NAND gates.
That using a single gate type, in this case NAND, will reduce the number of integrated circuits (IC) required to implement a logic circuit.
Introductory Slide / Overview of Presentation
AOI Logic
NAND Logic
More ICs = More $$
Less ICs = Less $$
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50. Universal Gate - NAND
Digital Electronics
2.2 Intro to NAND & NOR Logic
NAND Gate X Y X Y Z 1
Overview of basic NAND gate : Logic Symbol, Logic Expression (using DeMorgan’s) and Truth Table.
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51. NAND Gate as an Inverter Gate
Universal Gate - NAND
Digital Electronics
2.2 Intro to NAND & NOR Logic
NAND Gate as an Inverter Gate
(Before Bubble) X X Z 1
When you tie the inputs on a NAND gate together, the output will be the complement of the input.
Equivalent to Inverter
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52. NAND Gate as an AND Gate X Y X Y Z 1 NAND Gate Inverter
Universal Gate - NAND
Digital Electronics
2.2 Intro to NAND & NOR Logic
NAND Gate as an AND Gate X Y
NAND Gate
Inverter X Y Z 1
This one is easy to see, a NAND gate is an AND gate with the output inverted. So if you invert the output again, you will get an AND gate. Note that we are using a NAND gate for the inverter.
Equivalent to AND Gate
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53. NAND Gate as an OR Gate X Y X Y Z 1 NAND Gate Inverters
Universal Gate - NAND
Digital Electronics
2.2 Intro to NAND & NOR Logic
NAND Gate as an OR Gate X Y
NAND Gate
Inverters X Y Z 1
This one is a bit harder to see. If you invert both of the inputs of a NAND gate, you will get an OR gate. Note that we’re using NAND gates as inverters.
Equivalent to OR Gate
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54. NAND Gate Equivalent to AOI Gates
Universal Gate - NAND
Digital Electronics
2.2 Intro to NAND & NOR Logic
NAND Gate Equivalent to AOI Gates
AND OR
INVERTER
Summary of the three AOI gates and their NAND equivalent.
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55. Universal Gate – NOR This presentation will demonstrate…
Digital Electronics
2.2 Intro to NAND & NOR Logic
Universal Gate – NOR
This presentation will demonstrate…
The basic function of the NOR gate.
How an NOR gate can be using to replace an AND gate, an OR gate or an INVERTER gate.
How a logic circuit implemented with AOI logic gates could be re-implemented using only NOR gates
That using a single gate type, in this case NOR, will reduce the number of integrated circuits (IC) required to implement a logic circuit.
Introductory Slide / Overview of Presentation
AOI Logic
NOR Logic
More ICs = More $$
Less ICs = Less $$
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56. Universal Gate - NOR
Digital Electronics
2.2 Intro to NAND & NOR Logic
NOR Gate X Y X Y Z 1
Overview of basic NOR gate : Logic Symbol, Logic Expression (using DeMorgan’s) and Truth Table.
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57. NOR Gate as an Inverter Gate
Universal Gate - NOR
Digital Electronics
2.2 Intro to NAND & NOR Logic
NOR Gate as an Inverter Gate X
(Before Bubble) X Z 1
When you tie the inputs on a NOR gate together, the output will be the complement of the input.
Equivalent to Inverter
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58. NOR Gate as an OR Gate X Y X Y Z 1 NOR Gate “Inverter”
Universal Gate - NOR
Digital Electronics
2.2 Intro to NAND & NOR Logic
NOR Gate as an OR Gate X Y
NOR Gate
“Inverter” X Y Z 1
This one is easy to see, a NOR gate is in NOR gate with the output inverted. So if you invert the output again you will get an OR gate. Note we’re using a NOR gate for the inverter.
Equivalent to OR Gate
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59. NOR Gate as an AND Gate X Y X Y Z 1 NOR Gate “Inverters”
Universal Gate - NOR
Digital Electronics
2.2 Intro to NAND & NOR Logic
NOR Gate as an AND Gate X Y
“Inverters”
NOR Gate X Y Z 1
This one is a bit harder to see. If you invert both the inputs of a NOR gate you will get an AND gate. Note we’re using NOR gates as inverters.
Equivalent to AND Gate
Project Lead The Way, Inc.
Copyright 2009

60. NOR Gate Equivalent of AOI Gates
Universal Gate - NOR
Digital Electronics
2.2 Intro to NAND & NOR Logic
NOR Gate Equivalent of AOI Gates
AND OR
INVERTER
Summary of the three AOI gates and their NOR equivalent.
Project Lead The Way, Inc.
Copyright 2009

61. AOI Logic Implementation
Digital Electronics
2.1 Introduction to AOI Logic
AOI Logic Implementation
This presentation will demonstrate how to…
Design an AOI logic circuit from a Sum-Of- Products (SOP) logic expression.
Introductory Slide / Overview of Presentation
EQUALS
AOI Logic Circuit
Logic Expression
Project Lead The Way, Inc.
Copyright 2009

62. Designing AOI SOP Logic Circuits
AOI Logic Implementation
Digital Electronics
2.1 Introduction to AOI Logic
Designing AOI SOP Logic Circuits
Design Steps
Implement each Minterm in the logic expression with an AND gate with the same number of inputs as there are variables in the Minterm. (i.e., AB = 2 input gate, ABC = 3 input gate, ABCD = 4 input gate, etc.)
OR together the outputs of the AND gates to produce the logic expression.
If necessary, gates can be cascaded to create gates with more inputs.
Design Steps for SOP AOI logic designs.
Project Lead The Way, Inc.
Copyright 2009

63. Example #1: AOI Implementation SOP
AOI Logic Implementation
Digital Electronics
2.1 Introduction to AOI Logic
Example #1: AOI Implementation SOP
Example
Design an AOI Logic Circuit for the SOP logic expression shown below.
Pause the power point and allow the student to work on the example. The solution is on the next slide.
Project Lead The Way, Inc.
Copyright 2009

64. Example #2: AOI Implementation SOP
AOI Logic Implementation
Digital Electronics
2.1 Introduction to AOI Logic
Example #2: AOI Implementation SOP
Example
Unfortunately, in this class, we only have access to (2) input OR gates and (2) & (3) input AND gates. Limiting your design to these gates, redesign the AOI Logic Circuit for the SOP expression in the previous example.
Pause the power point and allow the student to work on the example. The solution is on the next slide.
Project Lead The Way, Inc.
Copyright 2009

65. Example #2: AOI Implementation SOP
AOI Logic Implementation
Digital Electronics
2.1 Introduction to AOI Logic
Example #2: AOI Implementation SOP
Example
Unfortunately, only (2) input OR gates and (2) & (3) AND gates exist in hardware. Limiting your design to these gates, redesign the AOI Logic Circuit for the SOP expression in the previous example.
Solution
The solution for example #2 is included on this slide. If you print handouts, do not print this page.
Project Lead The Way, Inc.
Copyright 2009