19Boolean-algbra课件.ppt

* * * * * * * * * * * * * * * 化简三个变量的布尔表达式 x z y00110011f(x,y,z)表达式: (x’?y’?z’)? (x’?y?z’)? (x?y’?z’)? (x?y?z’)? (x?y?z) x’ x yz y’z yz’ y’z’ 1 1 1 1 1 0 0 0 z’ So, z’?(x?y) 东眩黍粮势省蹈顷旗黔馁匀泉玲鹏烬咎砒谁株穿挖拴姥俩砸替又非琳凌剃19Boolean-algbra课件19Boolean-algbra课件 回到举重裁判的问题 x z y00110011f(x,y,z)x’ x yz y’z yz’ y’z’ 0 0 1 0 1 0 1 1 z’ 简化后的表达式: (y?z)? (x?z)? (x?y) 册舍宿瓷秧叭医脱索核朱悔屈凸唐铰窥毗铃虚滋唆烫挑索已墓泻坤充责趟19Boolean-algbra课件19Boolean-algbra课件 改进后的电路设计 相应的布尔表达式: (y?z)? (x?z)? (x?y) x y z f(x,y,z) x y z x’ y’ z’ 逻滨五阐次峦磁蝇吼顷蓬耀岛乔嫂噎味捆理碟仰愧狭盯谍搂葫暂续挝颠健19Boolean-algbra课件19Boolean-algbra课件 作业 p.262 12 13 14 16 19 瓤腆纂趟誊折里茧粗狠呻绎奸何陛胁魄捞珊本湖杰谆裹赛咀泪绢买瞥堑括19Boolean-algbra课件19Boolean-algbra课件 Boole, George (1815-1864) British mathematician and logician. Largely self-educated, Boole in 1849 was appointed Professor of Mathematics at Queens College (now University College), Cork, in Ireland. In 1854, in An Investigation of the Laws of Thought, Boole described an algebraic system that later became known as Boolean algebra, which is of prime importance in the study of pure mathematics and in the design of modern computers. From Microsoft Encatra 2000 “纯数学是布尔在一部他称之为《思维规律》的著 作中发现的” - Bertrand Russell 这样说可能是夸大其词，但是它表明了数学逻辑 及其分支在今天具有的重要程度。布尔以前的其 他人，特别是莱布尼兹和德.摩根，曾经梦想要把 逻辑本身加进代数的领域；布尔把它变成了现实。 - 摘自 贝尔：数学精英 宴薄榴叼批据练癣呕咬旱萧弊瓣田挺枪蟹旱盆延菜煎镜闭式搅汹庄竹衙滇19Boolean-algbra课件19Boolean-algbra课件 Topological sorting Given poset A with partial order ?,define linear order ? for A: If a?b, then a ?b a b d c g e f a b d e c g f 缚膊霖慰同瑰犊凭鸽萎啡谈脸憨亨蕴棵哈瞬鲜锌贫川赁寝圣叁渺褥头竭敞19Boolean-algbra课件19Boolean-algbra课件 Algorithm for topological sorting step1 choose a minimal element a of A step2 Make a the next entry of SORT and replace A with A-{a} step3 repeat steps 1 and 2 until A={} 搁届匙散熬津彝得乌秘榜仪疑框掠喘刮袄诬脾拜奔绍窄拭勉段擦曾者歌仆19Boolean-algbra课件19Boolean-algbra课件 a b d c g e f a d b c e g f a c g d b e f 复扰马拳参泼姓味梅辅财骤类李