Maria

EJERCICIOS
a- Dibujar el diagrama lógico por medio de la expresión booleana original
b- Listar la tabla de verdad para la función
c- Simplifique la expresión algebraica mediante el álgebrabooleana
d- Dibuje un diagrama lógico de la expresión simplificada y
e- Verifique mediante tabla de verdad
Para cada una de las siguientes funciones booleanas:
1. S = ABC + ABC' + AB'C

A | B | C| ABC+ | ABC’+ | AB’C | =S |
0 | 0 | 0 | 0 | 0 | 0 | 0 |
0 | 0 | 1 | 0 | 0 | 0 | 0 |
0 | 1 | 0 | 0 | 0 | 0 | 0 |
0 | 1 | 1 | 0 | 0 | 0 | 0 |
1 | 0 | 0 | 0 | 0 | 0 | 0 |
1 | 0 | 1 | 0 | 0 |1 | 1 |
1 | 1 | 0 | 0 | 1 | 0 | 1 |
1 | 1 | 1 | 1 | 0 | 0 | 1 |

Simplificar
S = ABC + ABC' + AB'C
AB (C+C’) +AB’C
AB+ABC
A (B+B’C)
A | B | C | A | (B+B’C) | =S |
0 | 0 | 0 | 0 | 0 | 0|
0 | 0 | 1 | 0 | 1 | 0 |
0 | 1 | 0 | 0 | 1 | 0 |
0 | 1 | 1 | 0 | 1 | 0 |
1 | 0 | 0 | 1 | 0 | 0 |
1 | 0 | 1 | 1 | 1 | 1 |
1 | 1 | 0 | 1 | 1 | 1 |
1 | 1 | 1 | 1 | 1 | 1 |

2. S = A’C(A'BD)' + A'BC'D' + AB'C
A | B | C | A’C | (A'BD)' | A'BC'D' | AB'C |
0 | 0 | 0 | 0 | 0 | 0 | 0 |
0 | 0 | 1 | 0 | 0 | 0 | 0 |
0 | 1 | 0 | 0 | 0 | 0 | 0 |
0 | 1 | 1 | 0 | 0 | 0 | 0 |
1 | 0| 0 | 0 | 0 | 0 | 0 |
1 | 0 | 1 | 0 | 0 | 1 | 1 |
1 | 1 | 0 | 0 | 1 | 0 | 1 |
1 | 1 | 1 | 1 | 0 | 0 | 1 |

Simplificación:
S=A`C (A+B’+D’) +A’BC’D’+AB’C
S=A’CA+AC’B’+A’C’D’+A’BC’D’+AB’CS=B’C (A’+A) + A’D ’(C+BC’)
S= B’C+A’D (B+C)

A | B | C | | ABC’+ | AB’C | =S |
0 | 0 | 0 | 0 | 0 | 0 | 0 |
0 | 0 | 1 | 0 | 0 | 0 | 0 |
0 | 1 | 0 | 0 | 0 | 0 | 0 |
0 | 1 | 1 | 0 | 0 | 0 | 0|
1 | 0 | 0 | 0 | 0 | 0 | 0 |
1 | 0 | 1 | 0 | 0 | 1 | 1 |
1 | 1 | 0 | 0 | 1 | 0 | 1 |
1 | 1 | 1 | 1 | 0 | 0 | 1 |

3. S = (A'+B)(A+B+D)D'

Simplificación:
(A’+B)(A+B+D)D’A’AD’+A’BD’+A’DD’+BAD’+BBD’
A’BD’+A’+BA’D’+BD’
BD’ (A’+A+1)
BD’

B | D | BD’ |
0 | 0 | 0 |
0 | 1 | 0 |
1 | 0 | 1 |
1 | 1 | 0 |

4. S = (A(AB)')'((AB)'B)'

A | B | (A(AB)')' |...