Porte logiche

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Gilda Tobia

Porte logiche fondamentali e Algebra di Boole reti combinatorie per sistemi a tre ingressi

Education

CIRCUITI LOGICI ISTITUTO ISTRUZIONE SECONDARIA SUPERIORE I.P.A.A. - A L C A M O Sede Associata I.P.S.I.A. – CALATAFIMI SEGESTA

Circuito A A S S I 2 I 1 0 1 L I 2 0 1 L I 1

Circuito serie I 1 I 2 L A S S S off off on on off on on off L I 2 I 1

Circuito parallelo I 1 I 2 L A A A S off off on on off on on off L I 2 I 1

TABELLE DELLA VERITA’ 0 1 1 0 NOT YES 0 1 y a 0 1 y a

TABELLE DELLA VERITA’ AND OR 0 1 0 0 0 1 1 1 0 0 1 1 0 1 1 0 y b a 0 0 1 1 0 1 1 0 y b a

TABELLE DELLA VERITA’ NOR 1 0 0 0 a b y 0 0 1 1 0 1 1 0 y b a

TABELLE DELLA VERITA’ NAND 1 1 1 0 a b y 0 0 1 1 0 1 1 0 y b a

PORTE LOGICHE NOT AND OR NAND NOR EXOR 1 &  & 

Algebra di Boole ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],ESEMPIO

Proprietà associativa (a + b ) + c a + ( b + c ) = 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 0 1 1 1 1 0 0 1 1 1 1 1 1 0 1 1 1 0 1 0 1 1 0 1 0 0 0 0 0 0 0 0 y (a+b)+c a+b c b a 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 0 1 1 1 0 0 0 1 1 1 1 1 1 0 1 1 1 0 1 0 1 1 1 1 0 0 0 0 0 0 0 0 y a+(b+c) b +c c b a

Proprietà commutativa (a + b) = (b + a) (a * b) = (b * a) 1 1 1 1 1 1 1 1 0 1 1 1 1 1 0 0 0 0 0 0 y b+a a+b b a 1 1 1 1 1 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 y b * a a * b b a

Proprietà assorbimento a+ (a*b) = a a*( a+b) = a 1 1 0 0 a+(a*b) 1 0 0 0 a*b 1 1 1 1 0 1 0 1 0 0 0 0 y b a 1 1 0 0 a*(a+b) 1 1 1 0 a+b 1 1 1 1 0 1 0 1 0 0 0 0 y b a

Proprietà assorbimento a+ (a*b) ( a+b) = 0 0 1 0 a*b 1 1 1 0 a+(a*b) 0 0 1 1 a 1 1 1 1 0 1 1 1 0 0 0 0 y b a 1 1 1 0 a+b 1 1 1 1 0 1 1 1 0 0 0 0 y b a

Proprietà assorbimento a* (a+b) ( a*b) = 1 0 1 1 a+b 1 0 0 0 a*(a+b) 0 0 1 1 a 1 1 1 0 0 1 0 1 0 0 0 0 y b a 1 0 0 0 a*b 1 1 1 0 0 1 0 1 0 0 0 0 y b a

Proprietà distributiva a + ( b * c) (a + b) * (a + c ) = 1 1 1 1 1 1 1 1 0 0 1 1 1 1 0 1 0 1 1 1 0 0 0 1 1 1 1 1 1 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 y a+ (b*c) b*c c b a 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 0 1 1 1 1 0 0 1 1 1 1 1 1 0 0 0 1 0 1 0 0 1 0 1 0 0 0 0 0 0 0 0 (a+b)*(a+c) a+c a + b c b a

Proprietà involuzione a = a 1 0 a 1 0 1 0 1 0 y a a

Proprietà idempotenza a + b = b + a a * b = b * a 1 1 1 0 b+a 1 1 1 0 0 0 0 0 1 1 1 1 1 1 0 1 a+b y b a 1 0 0 0 b*a 0 0 1 0 0 0 0 0 1 1 1 1 0 0 0 1 a*b y b a

Teorema del consenso (a*b )+(a*c)+(b*c) (a* b) +(a*c) = 1 0 0 0 1 0 0 0 b*c 0 0 0 0 1 1 1 1 a 1 0 1 1 1 1 1 0 1 0 1 1 0 0 0 1 0 1 0 0 0 0 0 1 1 1 0 1 1 0 0 0 0 0 1 0 1 1 0 1 0 0 0 0 0 0 0 0 y a*c a*b c b a 0 0 0 0 1 1 1 1 a 1 0 1 0 1 0 1 0 c 1 1 1 1 1 1 0 1 1 1 0 0 0 0 1 0 0 0 0 1 1 1 0 1 0 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0 y a*c a*b b a

Teorema del consenso (a+b )*(a+c)*(b+c) (a+ b) *(a+c) = 1 1 1 0 1 1 1 0 b+c 0 0 0 0 1 1 1 1 a 1 1 1 1 1 1 0 0 1 0 1 1 1 1 1 1 0 1 0 0 1 0 0 1 1 1 1 1 1 0 1 1 1 0 1 0 0 1 0 1 0 0 0 1 0 0 0 0 y a+c a+b c b a 0 0 0 0 1 1 1 1 a 1 0 1 0 1 0 1 0 c 1 1 1 1 1 0 0 1 1 1 1 1 1 0 1 0 0 1 0 1 1 1 1 1 0 1 1 1 1 0 0 1 0 0 0 0 1 0 0 0 y a+c a+b b a

Teorema di De Morgan a + b = a * b 0 0 0 1 a+b 0 1 1 0 1 0 0 0 0 1 1 1 0 1 0 1 a+b y b a 0 0 1 1 a 0 1 0 1 b 0 0 1 0 1 1 0 0 0 0 1 1 0 0 0 1 a * b y b a

Teorema di De Morgan a * b = a + b 0 1 1 1 a*b 1 0 1 0 1 0 0 0 0 1 1 1 1 0 0 1 a*b y b a 0 0 1 1 a 0 1 0 1 b 1 1 1 0 1 1 0 0 0 0 1 1 1 1 0 1 a + b y b a

Teorema di Shannon f (x 1 , x 2 , x 3 , x 4 …. x n ,* ) = f (x 1 , x 2 , x 3 , x 4 …. x n . +)

Tabella della Verità a 3 ingressi 1 0 0 0 1 1 0 1 1 1 1 0 1 1 1 0 1 0 0 1 1 1 0 0 1 0 1 0 0 0 0 0 y c b a

Tabella della Verità a 3 ingressi abc 0 0 0 abc abc 0 abc 1 1 1 0 1 1 1 0 1 0 0 1 1 1 0 0 1 0 1 0 0 0 0 0 y c b a

Tabella della Verità a 3 ingressi abc + abc + abc + abc y = bc + ac y =

Tabella della Verità a 3 ingressi bc + ac y = a b c & & Rete combinatoria 

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Porte logiche

1. CIRCUITI LOGICI ISTITUTO ISTRUZIONE SECONDARIA SUPERIORE I.P.A.A. - A L C A M O Sede Associata I.P.S.I.A. – CALATAFIMI SEGESTA

2. Circuito A A S S I 2 I 1 0 1 L I 2 0 1 L I 1

3. Circuito serie I 1 I 2 L A S S S off off on on off on on off L I 2 I 1

4. Circuito parallelo I 1 I 2 L A A A S off off on on off on on off L I 2 I 1

5. TABELLE DELLA VERITA’ 0 1 1 0 NOT YES 0 1 y a 0 1 y a

6. TABELLE DELLA VERITA’ AND OR 0 1 0 0 0 1 1 1 0 0 1 1 0 1 1 0 y b a 0 0 1 1 0 1 1 0 y b a

7. TABELLE DELLA VERITA’ NOR 1 0 0 0 a b y 0 0 1 1 0 1 1 0 y b a

8. TABELLE DELLA VERITA’ NAND 1 1 1 0 a b y 0 0 1 1 0 1 1 0 y b a

9. PORTE LOGICHE NOT AND OR NAND NOR EXOR 1 &  & 

10.

11. Proprietà associativa (a + b ) + c a + ( b + c ) = 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 0 1 1 1 1 0 0 1 1 1 1 1 1 0 1 1 1 0 1 0 1 1 0 1 0 0 0 0 0 0 0 0 y (a+b)+c a+b c b a 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 0 1 1 1 0 0 0 1 1 1 1 1 1 0 1 1 1 0 1 0 1 1 1 1 0 0 0 0 0 0 0 0 y a+(b+c) b +c c b a

12. Proprietà commutativa (a + b) = (b + a) (a * b) = (b * a) 1 1 1 1 1 1 1 1 0 1 1 1 1 1 0 0 0 0 0 0 y b+a a+b b a 1 1 1 1 1 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 y b * a a * b b a

13. Proprietà assorbimento a+ (a*b) = a a*( a+b) = a 1 1 0 0 a+(a*b) 1 0 0 0 a*b 1 1 1 1 0 1 0 1 0 0 0 0 y b a 1 1 0 0 a*(a+b) 1 1 1 0 a+b 1 1 1 1 0 1 0 1 0 0 0 0 y b a

14. Proprietà assorbimento a+ (a*b) ( a+b) = 0 0 1 0 a*b 1 1 1 0 a+(a*b) 0 0 1 1 a 1 1 1 1 0 1 1 1 0 0 0 0 y b a 1 1 1 0 a+b 1 1 1 1 0 1 1 1 0 0 0 0 y b a

15. Proprietà assorbimento a* (a+b) ( a*b) = 1 0 1 1 a+b 1 0 0 0 a*(a+b) 0 0 1 1 a 1 1 1 0 0 1 0 1 0 0 0 0 y b a 1 0 0 0 a*b 1 1 1 0 0 1 0 1 0 0 0 0 y b a

16. Proprietà distributiva a + ( b * c) (a + b) * (a + c ) = 1 1 1 1 1 1 1 1 0 0 1 1 1 1 0 1 0 1 1 1 0 0 0 1 1 1 1 1 1 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 y a+ (b*c) b*c c b a 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 0 1 1 1 1 0 0 1 1 1 1 1 1 0 0 0 1 0 1 0 0 1 0 1 0 0 0 0 0 0 0 0 (a+b)*(a+c) a+c a + b c b a

17. Proprietà involuzione a = a 1 0 a 1 0 1 0 1 0 y a a

18. Proprietà idempotenza a + b = b + a a * b = b * a 1 1 1 0 b+a 1 1 1 0 0 0 0 0 1 1 1 1 1 1 0 1 a+b y b a 1 0 0 0 b*a 0 0 1 0 0 0 0 0 1 1 1 1 0 0 0 1 a*b y b a

19. Teorema del consenso (a*b )+(a*c)+(b*c) (a* b) +(a*c) = 1 0 0 0 1 0 0 0 b*c 0 0 0 0 1 1 1 1 a 1 0 1 1 1 1 1 0 1 0 1 1 0 0 0 1 0 1 0 0 0 0 0 1 1 1 0 1 1 0 0 0 0 0 1 0 1 1 0 1 0 0 0 0 0 0 0 0 y a*c a*b c b a 0 0 0 0 1 1 1 1 a 1 0 1 0 1 0 1 0 c 1 1 1 1 1 1 0 1 1 1 0 0 0 0 1 0 0 0 0 1 1 1 0 1 0 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0 y a*c a*b b a

20. Teorema del consenso (a+b )*(a+c)*(b+c) (a+ b) *(a+c) = 1 1 1 0 1 1 1 0 b+c 0 0 0 0 1 1 1 1 a 1 1 1 1 1 1 0 0 1 0 1 1 1 1 1 1 0 1 0 0 1 0 0 1 1 1 1 1 1 0 1 1 1 0 1 0 0 1 0 1 0 0 0 1 0 0 0 0 y a+c a+b c b a 0 0 0 0 1 1 1 1 a 1 0 1 0 1 0 1 0 c 1 1 1 1 1 0 0 1 1 1 1 1 1 0 1 0 0 1 0 1 1 1 1 1 0 1 1 1 1 0 0 1 0 0 0 0 1 0 0 0 y a+c a+b b a

21. Teorema di De Morgan a + b = a * b 0 0 0 1 a+b 0 1 1 0 1 0 0 0 0 1 1 1 0 1 0 1 a+b y b a 0 0 1 1 a 0 1 0 1 b 0 0 1 0 1 1 0 0 0 0 1 1 0 0 0 1 a * b y b a

22. Teorema di De Morgan a * b = a + b 0 1 1 1 a*b 1 0 1 0 1 0 0 0 0 1 1 1 1 0 0 1 a*b y b a 0 0 1 1 a 0 1 0 1 b 1 1 1 0 1 1 0 0 0 0 1 1 1 1 0 1 a + b y b a

23. Teorema di Shannon f (x 1 , x 2 , x 3 , x 4 …. x n ,* ) = f (x 1 , x 2 , x 3 , x 4 …. x n . +)

24. Tabella della Verità a 3 ingressi 1 0 0 0 1 1 0 1 1 1 1 0 1 1 1 0 1 0 0 1 1 1 0 0 1 0 1 0 0 0 0 0 y c b a

25. Tabella della Verità a 3 ingressi abc 0 0 0 abc abc 0 abc 1 1 1 0 1 1 1 0 1 0 0 1 1 1 0 0 1 0 1 0 0 0 0 0 y c b a

26. Tabella della Verità a 3 ingressi abc + abc + abc + abc y = bc + ac y =

27. Tabella della Verità a 3 ingressi bc + ac y = a b c & & Rete combinatoria 

Porte logiche

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