Department of Computer Engineering. 2 Engr Ahmad Bilal M IN AND MAX Term Khabi Gharoor Nahi Kiya.
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Transcript of Department of Computer Engineering. 2 Engr Ahmad Bilal M IN AND MAX Term Khabi Gharoor Nahi Kiya.
Department of Computer Engineering
Engr. Ahmad B i la lahmadb i la l .engr@gmai l . com
2
Engr Ahmad Bilal
M IN AND MAX Term
Khabi Gharoor
Nahi Kiya
Department of Computer Engineering
Engr. Ahmad B i la lahmadb i la l .engr@gmai l . com
Today's GoalSolve the surprise Quiz at
the end of slides
Department of Computer Engineering
Engr. Ahmad B i la lahmadb i la l .engr@gmai l . com
SOP and POS
Q1 :Why Standard SOP and POS forms?Q2 How can Be Implemented?
Can be implemented using AND and OR Functions
Department of Computer Engineering
Engr. Ahmad B i la lahmadb i la l .engr@gmai l . com
Why to Use ThemMinimal Circuit
implementation by switching between Standard SOP or POS
Department of Computer Engineering
Engr. Ahmad B i la lahmadb i la l .engr@gmai l . com
• AB+ABC• ABX+DFE’+GHJ
• (A+B)(F+G)• (X+A+F+T)(A+A)
Example
Department of Computer Engineering
Engr. Ahmad B i la lahmadb i la l .engr@gmai l . com
PROBLEM
• Issues With Boolean Algebra• Become Tough• Need Expertise
Department of Computer Engineering
Engr. Ahmad B i la lahmadb i la l .engr@gmai l . com
GETTING READY FOR K MAP
• Glossary• Minterms: Product terms in Standard SOP
form• Maxterms: Sum terms in Standard POS form
Department of Computer Engineering
Engr. Ahmad B i la lahmadb i la l .engr@gmai l . com
A B C Min-terms
Max-terms
0 0 0
0 0 1
0 1 0
0 1 1
1 0 0
1 0 1
1 1 0
1 1 1
Minterms and Maxterm
CBA .. CBA
CBA .. CBA
CBA .. CBA
CBA .. CBA
CBA .. CBA
CBA .. CBA
CBA .. CBA
CBA .. CBA
Department of Computer Engineering
Engr. Ahmad B i la lahmadb i la l .engr@gmai l . com
SO What The Use. How it helps to design us a
particular Circuit
Department of Computer Engineering
Engr. Ahmad B i la lahmadb i la l .engr@gmai l . com
Designing
• Lets say we want to design a Circuit who gives out put 1, on our desired inputs only using SOPs
Department of Computer Engineering
Engr. Ahmad B i la lahmadb i la l .engr@gmai l . com
Designing
• Remember its SOP• Define Inputs for which You want output as 1• For this example lets say the inputs are • 0,2,3,5,7
Department of Computer Engineering
Engr. Ahmad B i la lahmadb i la l .engr@gmai l . com
Implementing CCT SOPs
• Canonical Sum
CBA ,,
)7,5,3,2,0(,, CBA
Department of Computer Engineering
Engr. Ahmad B i la lahmadb i la l .engr@gmai l . com
0 2 3 5 7 000 010 011 101 111 A’.B’.C’+A’BC’+A’BC+AB’C+ABC
)7,5,3,2,0(,, CBA
NOW LOOKING AT THE ABOVE EQUATION DRAW A TRUTH TABLE
Department of Computer Engineering
Engr. Ahmad B i la lahmadb i la l .engr@gmai l . com
SOP-Equation and Truth Table ExpressionABCCBACBABCA )7,5,4,3(,, CBA
Input Output
A B C F
0 0 0 0
0 0 1 0
0 1 0 0
0 1 1 1
1 0 0 1
1 0 1 1
1 1 0 0
1 1 1 1
Department of Computer Engineering
Engr. Ahmad B i la lahmadb i la l .engr@gmai l . com
• POS can be Implemented in same way.• Lets say we want to design a circuits using POS
which gives 0 on only selected inputs• For Our Practice Let the inputs be 1 4 6
What about POS
Department of Computer Engineering
Engr. Ahmad B i la lahmadb i la l .engr@gmai l . com
Canonical Product
001 100 110
)6,4,1(,, CBA
)6,4,1(,, CBA
)CBA)(CBA)(CBA(
Department of Computer Engineering
Engr. Ahmad B i la lahmadb i la l .engr@gmai l . com
Conversions
= )6,4,1(,, CBA)7,5,3,2,0(,, CBA
Department of Computer Engineering
Engr. Ahmad B i la lahmadb i la l .engr@gmai l . com
aaDDDDDDDDDDDDEW2`PRACTICE QUESTIONDevelop a Booliean equation, Circuit diagram and Its truth table which gives 0 only on
following inputs1,2,3,5
Department of Computer Engineering
Engr. Ahmad B i la lahmadb i la l .engr@gmai l . com
POS-Truth Table Conversion )5,3,2,1(,, CBA
))()()(( CBACBACBACBA Input Output
A B C F
0 0 0 1
0 0 1 0
0 1 0 0
0 1 1 0
1 0 0 1
1 0 1 0
1 1 0 1
1 1 1 1
Department of Computer Engineering
Engr. Ahmad B i la lahmadb i la l .engr@gmai l . com
• Design a Lock• The Code of this lock is
last 3 digits of your Roll Number
• The Lock will only operate when its get output from the key pads in form of 101
• Proof with four samples of truth table, that your circuit works only for right code
1
1
Bonus QuestionThe Three input from key pads are given to XOR gate. The lock will only open when xor gives out put of 1 to gate
0