application of boolean algebra(minterms & maxterms)

7/25/2019 Application of Boolean Algebra(Minterms & Maxterms)

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APPLICATION OF BOOLEAN ALGE

(MINTERMS & MAXTERMS EXPAN

…NOUSHEEN ARSHAD...

...R1F15 BSCS 0040...

...PUNJAB UNIVERSITY (RWP CAMPUS)...



: M I N T

E R M S

:

• A MINTERM (PRODUCT) IS A COMBINATION OF VARIAB

• IT HAS A VALUE OF 1 FOR ONLY ONE INPUT COMBINATIO

• IT IS 0 FOR ALL THE OTHER COMBINATIONS OF VARIABL

• A MINTERM OF N VARIABLES IS THE PRODUCT OF N LI

WHICH EACH VARIABLE APPEARS ONCE IN EITHER A

COMPLEMENTED OR UNCOMPLEMENTED FORM.

• FOR EXAMPLE: IF A FUNCTION OF 3 VARIABLES X,Y A

PRODUCES AS 1 OUTPUT FOR XYZ010, 100, 111, THEN IT

WRITTEN AS F X!YZ!" XY!Z!" XYZ.



: M I N T

E R M S

E X P A

N S I O N

:

• IF A MINTERM HAS A SIN#LE 1 AND

THE REMAININ# CELLS AS 0!S, IT

WOULD APPEAR TO COVER A

MINIMUM AREA OF 1!S.

• IT IS STANDARD SUM$OF$PRODUCTS

(SOP).• F A!BC"AB!C!"AB!C"ABC HAS FOUR

MINTERMS.

• THIS FUNCTION WILL BE WRITTEN

AS

F % M(3,&,',).



: EXAMPLE :



: M A X T E

R M S :

• A MAX (SUM) TERM IS ALSO A UNIQUE COMBINATION OF

VARIABLES :

• HOWEVER, IT IS OPPOSITE OF MINTERMS.

• IT HAS A VALUE OF 0 FOR ONLY ONE INPUT COMBINAT

• IT IS 1 FOR ALL THE OTHER COMBINATIONS OF VARIA

• THAT IS WHY, IT IS CALLED MAX (SUM) TERMS.

FOR EXAMPLE THE SAME FUNCTION OF 3 VARIABLESZ PRODUCES AS 0 OUTPUT FOR XYZ000, 001, 011, 101, 11

F (X"Y"Z).(X"Y"Z!).(X"Y!"Z!).(X!"Y"Z!).(X!"Y!"Z)



: M A X T E

R M S

E X P

A N S I O

N :

• IT IS A STANDARD PRODUCTOF SUM (POS).

• WE CAN ALSO TREAT ANORDER OF VARIABLES TOREPRESENT AN INTE!ER .

• THE FUNCTION CAN ALSO BEWRITTEN AS F(X"Y"#) $ %M(0"1"&"5"').



: EXAMPLE :



: CONVERSION OF ENGLISH SENTENCE

BOOLEAN EQUATIONS :

• FOR SIMPLE PROBLEMS, O DIRECTLY FROM A WORD DESC THE DESIRED CIRCUIT BEHAVIOR TO AN BOOLEAN EXPRESS

• FOR EXAMPLE

• THE ALARM WILL RIN (!) IFF

• THE ALARM IS TURNED ON (A), AND

• THE DOOR IS NOT CLOSED (B"), OR• OR, IT IS AFTER # P.M (C), AND

• THE WINDOW IS NOT CLOSED (D").

• ! $ AB"%CD".



: COMBINATIONAL LOGIC DESIG

USING A TRUTH TABLE :

• EXAMPLE NO 01:• THE CANONICAL MINTERM (SOP) FORM F A!B!"A!B.

• THE CANONICAL MAXTERM (POS) FORM F (A!"B).(A!"B!).



: EXAMPLE NO 02 :

• MAXTERM EXPANSION• F(A,B,C) $ (A%B%C).(A%B%C").(A%B"%C)

$ M0 % M1% M&.

$ ' M(0,1,&).

• MINTERM EXPANSION

•F(A,B,C) $A"BC%AB"C"%AB"C%ABC"%ABC.

$ M3%M%M%M#%M*.

$ + M(3,,,#,*).



: DESIGN OF BINARY ADDERS

• DESIN SIMPLE BINARY ADDERS THAT ADDS TWOBIT BINA

(N1, N&) AND PRODUCES 3BIT SUM (N3).



: BINARY ADDER :

• 1 BIT BINARY ADDER...

• INPUTS: A,B, CARRY-IN.

• OUTPUT: SUM, CARRY-OUT.

• SUM = A'B'CIN + A'BCIN' + AB'CIN' + ABCIN.

• COUT = A'BCIN + AB'CIN + ABCIN' + ABCIN.• BOTH SUM AND COUT CAN BE MINIMIZED.

application of boolean algebra(minterms & maxterms)

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