Upload
khaya-ntuthuzelo-dwaza
View
266
Download
0
Embed Size (px)
Citation preview
After completing this study unit you should:
Be Able to demonstrate understanding and application of the logic operators and gates
Be able to demonstrate understanding and application of Inverter, AND gate & OR gate
Outcomes
DSYS1 M2U1 rev14-02 2
The Distinctive Shape Logic Symbol For The Inverter Is Shown Below
Inputs ► Left Of Shape; Outputs ► To Right
The Inverter
DSYS1 M2U1 rev14-02 3
Inverter Symbols
The Rectangular Outline Symbol For The Inverter is shown below
These Are Used In Many Publications
The Inverter
DSYS1 M2U1 rev14-02 4
Rectangular Inverter Symbols
1 1
Negation Indicator “O” Indicates Inversion On That Input Or Output
“O” Means 0 Is The Active Or Asserted Input / Output
The “Triangle” Symbol Used For Rectangular Symbols
Negation Indicators
DSYS1 M2U1 rev14-02 5
Truth Table ► Shows The Output Of A Logic Gate Or Circuit For All Possible Inputs Combinations
Inverter Truth Table
DSYS1 M2U1 rev14-02 6
in out
Input OutputLOW (0) HIGH(1)HIGH(1) LOW(0)
Inverter Truth Table
Timing Diagram – Shows Input And Output Waveforms In Relation To One Another In Time
Inverter Timing Diagram
DSYS1 M2U1 rev14-02 7
Inverter Timing Diagram
Input
Output
Boolean Algebra Is Used To Mathematically Describe A Logic Gate Or Circuit
Variables Are Used In These Equations And Can Have A Value Of 0 Or 1
Variable Used Are: A, B, C … For Inputs And X, Y, Z, Q For Outputs
Boolean Algebra
DSYS1 M2U1 rev14-02 8
The Compliment Of A Variable Is Equal To The Inverse Of The Variable◦ (Variable=1 ► Compliment Of The Variable =0)
Inverter Expression
DSYS1 M2U1 rev14-02 9
A X
AX :Expression Boolean
Inverters May Be Used To Derive The 1’s Compliment Of A Binary Number◦ 74LS04 (Hex Inverter)
Inverter Application
DSYS1 M2U1 rev14-02 10
1 0 1 1 Binary Number
0 1 0 0 1’s Compliment
Logic Gate ► Circuit That Performs A Basic Logic Operation
AND Gate ► Has Two Or More Inputs And A Single Output
The AND Gate
DSYS1 M2U1 rev14-02 11
Distinctive Shape
Rectangular Outline
&
AND Gate ► Produces A HIGH Output Only If All Its Inputs Are HIGH, Otherwise It Puts Out LOW
AND Gate Operation
DSYS1 M2U1 rev14-02 12
00
0 10
0
01
0 11
1
For n Input-variables There Are 2n Possible Input Combinations
AND Gate Truth Table
DSYS1 M2U1 rev14-02 13
AB
X
A B X0 0 00 1 01 0 01 1 1
2-Input AND Truth Table
Complete The Truth Table For The 3-Input AND Gate Below
AND Gate Truth Table
DSYS1 M2U1 rev14-02 14
A B C X0 0 0 00 0 1 00 1 0 00 1 1 01 0 0 01 0 1 01 1 0 01 1 1 1AND Gate Truth
Table
ABC
X
In Majority Of Applications The Inputs To A Gate Are Not Static Levels But Changing Waveforms
Such Waveforms Are Broken Down Into “Static Sections” And Then The Truth Table Can Be Applied To These Sections
Pulsed Gate Operation
DSYS1 M2U1 rev14-02 15
AND ► Boolean Multiplication◦ 0 · 0 = 0◦ 0 · 1 = 0◦ 1 · 0 = 0◦ 1 · 1 = 1
X = A · B
◦ 74LS08 (Quad 2-Input) 74LS11 (Triple 3-Input)
AND Expression
DSYS1 M2U1 rev14-02 18
AB
X
AND Gate Is Commonly Use To Enable Signals To Pass From One Point To Another Or At Times To Inhibit Them ◦ See Frequency Counter & Seat Belt Alarm
AND Gate Application
DSYS1 M2U1 rev14-02 19
0 01
OR Gate ► Has Two Or More Inputs And A Single Output
The OR Gate
22
Rectangular Outline
1
Distinctive Shape
DSYS1 M2U1 rev14-02
OR Gate – Produces A HIGH Output If Any Of Its Inputs Are HIGH, And Only Puts Out A LOW All The Inputs Are LOW
The OR Gate
23
00
0 10
1
01
1 11
1
DSYS1 M2U1 rev14-02
Complete The Truth Table For The 3-Input OR Gate Below
OR Gate Truth Table
25
A B C X0 0 0 00 0 1 10 1 0 10 1 1 11 0 0 11 0 1 11 1 0 11 1 1 1
OR Gate Truth Table
ABC
X
DSYS1 M2U1 rev14-02
OR ► Boolean Addition (Not Same As Normal Addition)◦ 0 + 0 = 0◦ 0 + 1 = 1◦ 1 + 0 = 1◦ 1 + 1 = 1
X = A + B
OR Gate Expression
28 DSYS1 M2U1 rev14-02