Formulario Álgebra Booleana y Flip-Flops básicos
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Examen Final: Formulario Jos´ e Jaime Paredes Peralta 11 de mayo de 2015 Teoremas de ´ Algebra Booleana A +0 = A A + B = B + A A +(B + C ) = (A + B)+ C A + BC = (A + B)(A + C ) A + A = 1 A + A = A A +1 = 1 A + AB = A A + AB = A + B A + B = A B AB + AC + BC = AB + AC AB + A B = A AB + A BC = AB + AC AB + AC = (A + C )( A + B) A1 = A AB = BA A(BC ) = (AB)C A(B + C ) = AB + AC A A = 0 AA = A A0 = 0 A(A + B) = A A + B) = AB (AB) = A + B (A + B)( A + C )(B + C ) = (A + B)( A + C ) (A + B)(A + B) = A (A + B)(A + B + C ) = (A + B)(A + C ) (A + B)( A + C ) = AC + AB Flip-Flops Tabla 1: Tablas de verdad Flip-Flops S R f J K f T f D f 0 0 hold 0 0 hold 0 hold 0 reset 0 1 reset 0 1 reset 1 toggle 1 set 1 0 set 1 0 set 1 1 DC 1 1 toggle SR: Q + = S + RQ JK: Q + = KQ + J Q T: Q + = T Q + TQ D: Q + = D
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Formulario
Transcript of Formulario Álgebra Booleana y Flip-Flops básicos
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Examen Final: Formulario
Jose Jaime Paredes Peralta
11 de mayo de 2015
Teoremas de Algebra Booleana
A+ 0 = AA+B = B + A
A+ (B + C) = (A+B) + C
A+BC = (A+B)(A+ C)
A+ A = 1A+ A = AA+ 1 = 1
A+ AB = A
A+ AB = A+B
A+B = A B
AB + AC +BC = AB + AC
AB + AB = A
AB + ABC = AB + AC
AB + AC = (A+ C)(A+B)
A1 = AAB = BA
A(BC) = (AB)C
A(B + C) = AB + AC
AA = 0AA = AA0 = 0
A(A+B) = A
A+B) = AB
(AB) = A+B
(A+B)(A+ C)(B + C) = (A+B)(A+ C)
(A+B)(A+B) = A
(A+B)(A+B + C) = (A+B)(A+ C)
(A+B)(A+ C) = AC + AB
Flip-Flops
Tabla 1: Tablas de verdad Flip-FlopsS R f J K f T f D f
0 0 hold 0 0 hold 0 hold 0 reset0 1 reset 0 1 reset 1 toggle 1 set1 0 set 1 0 set1 1 DC 1 1 toggle
SR: Q+ = S +RQ
JK: Q+ = KQ+ JQ
T: Q+ = TQ+ TQ
D: Q+ = D
