Final Exam Review Wade Fife ECEn/CS 224 August 13, 2007 August 13, 2007.
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Transcript of Final Exam Review Wade Fife ECEn/CS 224 August 13, 2007 August 13, 2007.
Final Exam ReviewFinal Exam Review
Wade FifeWade Fife
ECEn/CS 224ECEn/CS 224
August 13, 2007August 13, 2007
2
Loose EndsLoose Ends
• Check your grades onlineCheck your grades online
• Weighting of grades and breakdown found Weighting of grades and breakdown found on syllabuson syllabus– A curve will be applied if neededA curve will be applied if needed
• Labs 9-12 should be graded by end of Labs 9-12 should be graded by end of weekweek
• Estimate your missing scores and you Estimate your missing scores and you should be able to calculate your gradeshould be able to calculate your grade
3
Exam SummaryExam Summary
• Do NOT write on exam!Do NOT write on exam!– Bring scratch paperBring scratch paper– Throw it away before leaving the testing centerThrow it away before leaving the testing center
• 50 Questions50 Questions– 1-17: True/False, 1 point each1-17: True/False, 1 point each– 18-25: Multiple choice, 1 point each18-25: Multiple choice, 1 point each– 26-50: Multiple choice, 3 points each26-50: Multiple choice, 3 points each
• 4 hour time limit4 hour time limit• Some reference material providedSome reference material provided• Wednesday and Thursday in the Testing CenterWednesday and Thursday in the Testing Center
– 8:00 am to 8:00 pm (tests collected at 9:00 pm)8:00 am to 8:00 pm (tests collected at 9:00 pm)
4
Study TipsStudy Tips
• Review topics onlineReview topics online• Previous semesters’ review slides onlinePrevious semesters’ review slides online• Midterm exam study questionsMidterm exam study questions• Homework solutions onlineHomework solutions online• Come see me to go over past tests, ask Come see me to go over past tests, ask
questionsquestions– Wednesday, 8:00 am to 5:00 pmWednesday, 8:00 am to 5:00 pm– Other times by appointment (email me first)Other times by appointment (email me first)– Room 435 CBRoom 435 CB
5
New for the Final ExamNew for the Final Exam
• Equivalent gatesEquivalent gates– An application of DeMorgan’s laws, truth An application of DeMorgan’s laws, truth
tablestables
• Excitation tablesExcitation tables• Flip flops with control inputsFlip flops with control inputs• FET operations and gates built from FETsFET operations and gates built from FETs• Need to have FF behavior memorized (D, Need to have FF behavior memorized (D,
T, JK)T, JK)• Possibly others…Possibly others…
6
Quick ReviewQuick Review
• FPGAsFPGAs• ROMsROMs• Mealy vs. MooreMealy vs. Moore• State encoding impact on circuitsState encoding impact on circuits• LC-3LC-3• VerilogVerilog• Bit order in questions and answersBit order in questions and answers
– QQ33QQ22QQ11QQ00 is different from Q is different from Q00QQ11QQ22QQ33
– Pay attention to the notation used!Pay attention to the notation used!
7
K-mapsK-maps• Give the minimum SOP expression for the function Give the minimum SOP expression for the function
F(A,B,C,D,E) = F(A,B,C,D,E) = m(2,5,7,12,13,14,15,16,17,18,22,23,24,25,26,28,29,30,31)m(2,5,7,12,13,14,15,16,17,18,22,23,24,25,26,28,29,30,31)
DEDE
BCBC0000 0101 1111 1010
0000
0101
1111
1010
A = 0A = 0
DEDE
BCBC0000 0101 1111 1010
0000
0101
1111
1010
A = 1A = 1
8
K-mapsK-maps• Give the minimum SOP expression for the function Give the minimum SOP expression for the function
F(A,B,C,D,E) = F(A,B,C,D,E) = m(2,5,7,12,13,14,15,16,17,18,22,23,24,25,26,28,29,30,31)m(2,5,7,12,13,14,15,16,17,18,22,23,24,25,26,28,29,30,31)
DEDE
BCBC0000 0101 1111 1010
0000 11
0101 11 11
1111 11 11 11 11
1010
A = 0A = 0
DEDE
BCBC0000 0101 1111 1010
0000 11 11 11
0101 11 11
1111 11 11 11 11
1010 11 11 11
A = 1A = 1
9
K-mapsK-maps• Give the minimum SOP expression for the functionGive the minimum SOP expression for the function
DEDE
BCBC0000 0101 1111 1010
0000 11
0101 11 11
1111 11 11 11 11
1010
A = 0A = 0
DEDE
BCBC0000 0101 1111 1010
0000 11 11 11
0101 11 11
1111 11 11 11 11
1010 11 11 11
A = 1A = 1
10
K-mapsK-maps• Give the minimum SOP expression for the functionGive the minimum SOP expression for the function
DEDE
BCBC0000 0101 1111 1010
0000 11
0101 11 11
1111 11 11 11 11
1010
A = 0A = 0
DEDE
BCBC0000 0101 1111 1010
0000 11 11 11
0101 11 11
1111 11 11 11 11
1010 11 11 11
A = 1A = 1
F = BC + A’CE + B’C’DE’ + AC’D’ + …
Essential Prime Implicants
11
K-mapsK-maps• Give the minimum SOP expression for the functionGive the minimum SOP expression for the function
DEDE
BCBC0000 0101 1111 1010
0000 11
0101 11 11
1111 11 11 11 11
1010
A = 0A = 0
DEDE
BCBC0000 0101 1111 1010
0000 11 11 11
0101 11 11
1111 11 11 11 11
1010 11 11 11
A = 1A = 1
F = BC + A’CE + B’C’DE’ + AC’D’ + …
Essential Prime Implicants
12
K-mapsK-maps• Give the minimum SOP expression for the functionGive the minimum SOP expression for the function
DEDE
BCBC0000 0101 1111 1010
0000 11
0101 11 11
1111 11 11 11 11
1010
A = 0A = 0
DEDE
BCBC0000 0101 1111 1010
0000 11 11 11
0101 11 11
1111 11 11 11 11
1010 11 11 11
A = 1A = 1
F = BC + A’CE + B’C’DE’ + AC’D’ + ACD + …
Essential Prime Implicants
13
K-mapsK-maps• Give the minimum SOP expression for the functionGive the minimum SOP expression for the function
DEDE
BCBC0000 0101 1111 1010
0000 11
0101 11 11
1111 11 11 11 11
1010
A = 0A = 0
DEDE
BCBC0000 0101 1111 1010
0000 11 11 11
0101 11 11
1111 11 11 11 11
1010 11 11 11
A = 1A = 1
F = BC + A’CE + B’C’DE’ + AC’D’ + ACD + ADE’
Essential Prime Implicants
14
K-mapsK-maps• Give the minimum SOP expression for the functionGive the minimum SOP expression for the function
DEDE
BCBC0000 0101 1111 1010
0000 11
0101 11 11
1111 11 11 11 11
1010
A = 0A = 0
DEDE
BCBC0000 0101 1111 1010
0000 11 11 11
0101 11 11
1111 11 11 11 11
1010 11 11 11
A = 1A = 1
F = BC + A’CE + B’C’DE’ + AC’D’ + ACD + ADE’ … + ACD + AC’E’
Essential Prime Implicants
15
K-mapsK-maps• Give the minimum SOP expression for the functionGive the minimum SOP expression for the function
DEDE
BCBC0000 0101 1111 1010
0000 11
0101 11 11
1111 11 11 11 11
1010
A = 0A = 0
DEDE
BCBC0000 0101 1111 1010
0000 11 11 11
0101 11 11
1111 11 11 11 11
1010 11 11 11
A = 1A = 1
F = BC + A’CE + B’C’DE’ + AC’D’ + ACD + ADE’ … + ACD + AC’E’ … + ACD + ABE’Essential Prime Implicants
16
K-mapsK-maps• Give the minimum SOP expression for the functionGive the minimum SOP expression for the function
DEDE
BCBC0000 0101 1111 1010
0000 11
0101 11 11
1111 11 11 11 11
1010
A = 0A = 0
DEDE
BCBC0000 0101 1111 1010
0000 11 11 11
0101 11 11
1111 11 11 11 11
1010 11 11 11
A = 1A = 1
F = BC + A’CE + B’C’DE’ + AC’D’ + ACD + ADE’ … + ACD + AC’E’ … + ACD + ABE’ … + CDE + …
Essential Prime Implicants
17
K-mapsK-maps• Give the minimum SOP expression for the functionGive the minimum SOP expression for the function
DEDE
BCBC0000 0101 1111 1010
0000 11
0101 11 11
1111 11 11 11 11
1010
A = 0A = 0
DEDE
BCBC0000 0101 1111 1010
0000 11 11 11
0101 11 11
1111 11 11 11 11
1010 11 11 11
A = 1A = 1
Essential Prime Implicants
F = BC + A’CE + B’C’DE’ + AC’D’ + ACD + ADE’ … + ACD + AC’E’ … + ACD + ABE’ … + CDE + ADE’
18
K-mapsK-maps
• Essential prime implicants ARE also prime Essential prime implicants ARE also prime implicantsimplicants
• Many prime implicants may not be used in Many prime implicants may not be used in the final solutionthe final solution
19
K-mapsK-maps• Non-essential prime implicants (some unused)Non-essential prime implicants (some unused)
DEDE
BCBC0000 0101 1111 1010
0000 11
0101 11 11
1111 11 11 11 11
1010
A = 0A = 0
DEDE
BCBC0000 0101 1111 1010
0000 11 11 11
0101 11 11
1111 11 11 11 11
1010 11 11 11
A = 1A = 1
F = BC + A’CE + B’C’DE’ + AC’D’ + ACD + ADE’ … + ACD + AC’E’ … + ACD + ABE’ … + CDE + ADE’
20
K-mapsK-maps• Give the minimum Give the minimum POSPOS expression for the function expression for the function
DEDE
BCBC0000 0101 1111 1010
0000 11
0101 11 11
1111 11 11 11 11
1010
A = 0A = 0
DEDE
BCBC0000 0101 1111 1010
0000 11 11 11
0101 11 11
1111 11 11 11 11
1010 11 11 11
A = 1A = 1
21
K-mapsK-maps• Give the minimum Give the minimum POSPOS expression for the function expression for the function
DEDE
BCBC0000 0101 1111 1010
0000 00 00 00
0101 00 00
1111
1010 00 00 00 00
A = 0A = 0
DEDE
BCBC0000 0101 1111 1010
0000 00
0101 00 00
1111
1010 00
A = 1A = 1
22
K-mapsK-maps• Give the minimum Give the minimum POSPOS expression for the function expression for the function
DEDE
BCBC0000 0101 1111 1010
0000 00 00 00
0101 00 00
1111
1010 00 00 00 00
A = 0A = 0
DEDE
BCBC0000 0101 1111 1010
0000 00
0101 00 00
1111
1010 00
A = 1A = 1
F’ = A’BC’ + C’DE + A’C’D’ + A’B’CE’ + AB’CD’ (all are essential)F = (A’BC’ + C’DE + A’C’D’ + A’B’CE’ + AB’CD’)’F = (A+B’+C)(C+D’+E’)(A+C+D)(A+B+C’+E)(A’+B+C’+D), by DeMorgan’s
23
Timing DiagramsTiming Diagrams
A
B=1C=1
D
G
A
D
5ns
20ns 30ns
32ns
TypeType DelayDelay
AND2AND2 3 ns3 ns
OR2OR2 4 ns4 ns
G
24
Timing DiagramsTiming Diagrams
A
B=1C=1
D
G
F
E
A
D
E
F
G
5ns
8ns
12ns
20ns
23ns
30ns
33ns
27ns 37ns
35ns
32ns
39ns
TypeType DelayDelay
AND2AND2 3 ns3 ns
OR2OR2 4 ns4 ns
25
Transistor Level SchematicsTransistor Level Schematics
What is it?What is it?
aa bb cc outout
00 00 00
00 00 11
00 11 00
00 11 11
11 00 00
11 00 11
11 11 00
11 11 11
Assume positive logic
26
Transistor Level SchematicsTransistor Level Schematics
What is it?What is it?
aa bb cc outout
00 00 00 11
00 00 11 11
00 11 00 11
00 11 11 11
11 00 00 11
11 00 11 00
11 11 00 00
11 11 11 00
out = a’ + b’c’
Assume positive logic
27
A B
C D 00 01 11 10
00
01
11
10
Z (A,B,C,D) = m(3,5,10,11,12,15) + d(4,8,14)
Implementing Logic with MuxesImplementing Logic with Muxes
4-to-1MUX Z
A C
I0
I1
I2
I3
28
A B
C D 00 01 11 10
00 X 1 X
01 1
11 1 1 1
10 X 1
Z (A,B,C,D) = m(3,5,10,11,12,15) + d(4,8,14)
4-to-1MUX Z
A C
I0
I1
I2
I3
B
D’
1
B'
D
F = A’B’CD = (0)’B’(1)D = B’D
Implementing Logic with MuxesImplementing Logic with Muxes