布尔代数运算基础.ppt

10布尔代数 Boolean Algebra ◆1854 George Boole《 The laws of Though》 ◆1938 Claude shannon ◆源自网络,做过改动,不拥有版权 Valadon onry. ch Asposeslides for NET 4o dient P Evaluation only. Created with Aspose Slides for NET 4.0 dient Profilo 71 Copyright 2004-2017Aspose Pty L 10布尔代数 Boolean Algebra ◆例:由两个开关共同控制一盏灯:当灯是关闭时,敲 击任何一个开关都可以开灯;当灯是打开时,敲击任 何一个开关都可以关灯。 (a)Inverter b)OR gate (c)AND gat Valadon onry. ch Asposeslides for NET 4o dient P Evaluation only. Created with Aspose Slides for NET 4.0 dient Profilo 71 Copyright 2004-2017Aspose Pty L 10布尔代数 Boolean Algebra ry+xy Valadon onry. ch Asposeslides for NET 4o dient P Evaluation only. Created with Aspose Slides for NET 4.0 dient Profilo 71 Copyright 2004-2017Aspose Pty L 101布尔函数 Boolean functions ◆布尔代数提供{0,1}集合上的运算和规则。 ■补运算0=1,1=0 。布尔和0+0=00+1=1,1+0=1,1+1=1 0●0=0,0·1=0,1·0=0,1·1=1 布尔积 Valadon onry. ch Asposeslides for NET 4o dient P Evaluation only. Created with Aspose Slides for NET 4.0 dient Profilo 71 Copyright 2004-2017Aspose Pty L 101布尔函数 Boolean functions ◆设B={0,1},则B={(x1x2x1),x∈B,1S91是由0和构 成的所有n元有序列的集合。从B到B的函数称为n元布尔 历数。 ◆例:F(x,y)=x+y Valadon onry. ch Asposeslides for NET 4o dient P Evaluation only. Created with Aspose Slides for NET 4.0 dient Profilo 71 Copyright 2004-2017Aspose Pty L 10.1布尔函数 Boolean functions ●布尔表达式(关于变元x1x2…,xn) 0,1,x1,x2…,xn是布尔表达式 如果E1和E2是布尔表达式,则E1,E1+E2)和(E1E2)是布 尔函数 ◆例:F(x,y)=x+y·z Valadon onry. ch Asposeslides for NET 4o dient P Evaluation only. Created with Aspose Slides for NET 4.0 dient Profilo 71 Copyright 2004-2017Aspose Pty L 布尔代数恒等式 (1)交换律a+b=b+a,ab=ba (2)结合律(a+b)+c=a+(b+c)(ab)c=a(bc) 析取标准式:割集 (3)幂等律a+a=a,aa=a (4吸收律a+(ab)=a a(a+b)=a 合取标准式:径集 (5)分配律a(b+c=(ab)+(ac),a+(bc)=(a+b)(a+c) ()同一律a1=a,a+0=a (7)支配律a0=0,a+1=1 (8)互补律a+a=1,a·a=0 (9)双重否定律a=a (10)摩根律a+b=a,b,ab=a+b Valadon onry. ch Asposeslides for NET 4o dient P Evaluation only. Created with Aspose Slides for NET 4.0 dient Profilo 71 Copyright 2004-2017Aspose Pty L 101布尔函数 Boolean functions 例:证明: yz+x(xz )+y(2+1)+zx=y+zx Valadon onry. ch Asp