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



Today's GoalSolve the surprise Quiz at

the end of slides



SOP and POS

Q1 :Why Standard SOP and POS forms?Q2 How can Be Implemented?

Can be implemented using AND and OR Functions



Why to Use ThemMinimal Circuit

implementation by switching between Standard SOP or POS



• AB+ABC• ABX+DFE’+GHJ

• (A+B)(F+G)• (X+A+F+T)(A+A)

Example



PROBLEM

• Issues With Boolean Algebra• Become Tough• Need Expertise



GETTING READY FOR K MAP

• Glossary• Minterms: Product terms in Standard SOP

form• Maxterms: Sum terms in Standard POS form



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



SO What The Use. How it helps to design us a

particular Circuit



Designing

• Lets say we want to design a Circuit who gives out put 1, on our desired inputs only using SOPs



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



Implementing CCT SOPs

• Canonical Sum

CBA ,,

)7,5,3,2,0(,, CBA



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



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



• 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



Canonical Product

001 100 110

)6,4,1(,, CBA

)6,4,1(,, CBA

)CBA)(CBA)(CBA(



Conversions

= )6,4,1(,, CBA)7,5,3,2,0(,, CBA



aaDDDDDDDDDDDDEW2`PRACTICE QUESTIONDevelop a Booliean equation, Circuit diagram and Its truth table which gives 0 only on

following inputs1,2,3,5



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



SHOCK QUIZ



• 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

Documents

Department of Computer Engineering. 2 Engr Ahmad Bilal M IN AND MAX Term Khabi Gharoor Nahi Kiya