Exercices

Exercice

Prouvez la relation a + (b . c) = (a + b) . (a + c) en complétant ces deux tables de vérité :

a	b	c	b . c	a + (b . c)
0	0	0
0	0	1
0	1	0
0	1	1
1	0	0
1	0	1
1	1	0
1	1	1

et

a	b	c	a + b	a + c	(a + b) . (a + c)
0	0	0
0	0	1
0	1	0
0	1	1
1	0	0
1	0	1
1	1	0
1	1	1

Correction

Attention

En mathématiques, l'addition ne se distribue pas sur la multiplication, par exemple 1 + (1 x 1) vaut 2 tandis que (1 + 1) x (1 + 1) vaut 4.

Encore une fois, bien que le symbole + soit utilisé pour représenter l'opérateur OU, il ne s'agit pas d'une addition.

Exercice

Sur votre cahier, prouvez les formules de Morgan :
a + b = a . b et a . b = a + b

Exercice

1. Sur votre cahier, écrivez les tables de vérités de a . b + c et de (a . b) + (a . c)

2. Observez ci-dessous le schéma correspondant à l'expression a . b + c. Utilisez-le pour vérifier vos réponses.

3. Construisez le schéma correspondant à (a . b) + (a . c) et utilisez-le pour vérifier vos réponses.

{ "width":700, "height":400, "showToolbox":true, "toolbox":[ {"type":"DC"}, {"type":"LED"}, {"type":"Toggle"}, {"type":"NOT"}, {"type":"AND"}, {"type":"OR"} ], "devices":[ {"type":"Toggle","id":"dev0","x":232,"y":72,"label":"b","state":{"on":false}}, {"type":"AND","id":"dev1","x":328,"y":40,"label":"AND"}, {"type":"Toggle","id":"dev2","x":232,"y":144,"label":"c","state":{"on":false}}, {"type":"Toggle","id":"dev3","x":232,"y":8,"label":"a","state":{"on":false}}, {"type":"NOT","id":"dev4","x":328,"y":120,"label":"NOT"}, {"type":"OR","id":"dev5","x":440,"y":72,"label":"OR"}, {"type":"LED","id":"dev6","x":520,"y":72,"label":"s"}, {"type":"DC","id":"dev7","x":80,"y":72,"label":"Alimentation"} ], "connectors":[ {"from":"dev0.in0","to":"dev7.out0"}, {"from":"dev1.in0","to":"dev3.out0"}, {"from":"dev1.in1","to":"dev0.out0"}, {"from":"dev2.in0","to":"dev7.out0"}, {"from":"dev3.in0","to":"dev7.out0"}, {"from":"dev4.in0","to":"dev2.out0"}, {"from":"dev5.in0","to":"dev1.out0"}, {"from":"dev5.in1","to":"dev4.out0"}, {"from":"dev6.in0","to":"dev5.out0"} ] }

Réponse au 3.

{ "width":700, "height":200, "showToolbox":false, "devices":[ {"type":"AND","id":"dev0","x":328,"y":40,"label":"AND"}, {"type":"LED","id":"dev1","x":512,"y":104,"label":"s"}, {"type":"Toggle","id":"dev2","x":232,"y":144,"label":"c","state":{"on":false}}, {"type":"NOT","id":"dev3","x":312,"y":104,"label":"NOT"}, {"type":"Toggle","id":"dev4","x":232,"y":8,"label":"a","state":{"on":false}}, {"type":"OR","id":"dev5","x":440,"y":96,"label":"OR"}, {"type":"DC","id":"dev6","x":72,"y":56,"label":"Alimentation"}, {"type":"AND","id":"dev7","x":376,"y":152,"label":"AND"}, {"type":"Toggle","id":"dev8","x":232,"y":72,"label":"b","state":{"on":false}} ], "connectors":[ {"from":"dev0.in0","to":"dev4.out0"}, {"from":"dev0.in1","to":"dev8.out0"}, {"from":"dev1.in0","to":"dev5.out0"}, {"from":"dev2.in0","to":"dev6.out0"}, {"from":"dev3.in0","to":"dev4.out0"}, {"from":"dev4.in0","to":"dev6.out0"}, {"from":"dev5.in0","to":"dev0.out0"}, {"from":"dev5.in1","to":"dev7.out0"}, {"from":"dev7.in0","to":"dev3.out0"}, {"from":"dev7.in1","to":"dev2.out0"}, {"from":"dev8.in0","to":"dev6.out0"} ] }

Exercice

Quelques questions pour ceux qui ont besoin de s'entraîner sur les tables de vérités et/ou pour préparer une évaluation.