Aljabar Boolean
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The document discusses several laws and properties related to Boolean algebra including: 1) Associative laws which state that operations combine in predictable ways regardless of grouping. 2) Commutative laws which state that the order of operands does not change the result. 3) Idempotent laws which state that an operand combined with itself is itself. 4) Identity laws which define operands that do not change the value of other operands. 5) Absorption laws which define relationships between operands combined in different ways. 6) Dominance laws which define the effect of combining an operand with 1 or 0. 7) Involution laws which define the effect of applying a logical complement twice. 8) Complement laws
Aljabar Boolean
- 4. a b a.b 0 0 0 0 1 0 1 0 0 1 1 1 a b a + b 0 0 0 0 1 1 1 0 1 1 1 1
- 5. a 0 1 1 0
- 7. a B a ab a + ab a + b 0 0 1 0 0 0 0 1 1 1 1 1 1 0 0 0 1 1 1 1 0 0 1 1
- 10. a. Hukum Asosiatif (i) a + (b + c) = (a + b) + c (ii) a . (b . c) = (a . b) . c b. Hukum Komutatif (i) a + b = b + a (ii) a . b = b . A c. Hukum Idempoten (Hukum Perluasan) (i) a + a = a (ii) a . a = a d. Hukum Identitas (i) a + 0 = a (ii) a . 1 = a e. Hukum Absorbsi (i) a + ( a . b ) = a (ii) a ( a + b ) = a (iii) a + ( a . b ) = a + b (iv) a ( a + b ) = a.b f. Hukum dominansi (i) a.1 = a (ii) a+0 = a (iii) a+1 = 1 (iv) a . 0 = 0 g. Hukum involusi (i) (a) = a h. Hukum Komplementasi (i) a + a = 1 (ii) a . a = 0 i. Hukum distributif: (i) a + ( b . c ) = ( a + b ) ( a + c ) (ii) a ( b + c) = a . b + a . c j. Hukum De Morgan (i) (a + b) = a. b (ii) (a . b) = a + b
- 15. x y z f(x,y,z) = xyz + x 0 0 0 0 0 0 1 0 0 1 0 0 0 1 1 0 1 0 0 1 1 0 1 1 1 1 0 1 1 1 1 1
- 17. x y z f=xyz + xyz + xyg g =xz + xy 0 0 0 0 0 0 0 1 1 1 0 1 0 0 0 0 1 1 1 1 1 0 0 1 1 1 0 1 1 1 1 1 0 0 0 1 1 1 0 0
- 20. x y Minterm Maxterm Suku Lambang Suku Lambang 0 0 xy m0 x + y M0 0 1 xy m1 x + y M1 1 0 xy m2 x + y M2 1 1 xy m3 x + y M3
- 21. x y z Minterm Maxterm Suku Lambang Suku Lambang 0 0 0 xyz m0 x + y + z M0 0 0 1 xyz m1 x + y + z M1 0 1 0 xyz m2 x + y + z M2 0 1 1 xyz m3 x + y + z M3 1 0 0 xyz m4 x + y + z M4 1 0 1 xyz m5 x + y + z M5 1 1 0 xyz m6 x + y + z M6 1 1 1 xyz m7 x + y + z M7
- 22. x y z xyz xyz xyz f(x,y,z) 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 1 0 0 0 0 0 0 1 1 0 0 0 0 1 0 0 0 1 0 1 1 0 1 0 0 0 0 1 1 0 0 0 0 0 1 1 1 0 0 1 1
- 27. xy xy xy xy
- 28. xyz xyz xyz xyz xyz xyz xyz xyz
- 30. wxyz wxyz wxyz wxyz wxyz wxyz wxyz wxyz wxyz wxyz wxyz wxyz wxyz wxyz wxyz wxyz