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Click to edit Master title style,Click to edit Master text styles,Second level,Third level,Fourth level,Fifth level,IE7 Released,Machine Structures,Lecture 15,组合逻辑电路的表示, week,after more than 3 years since the last major update,Microsoft finally releases the next generation of their Internet Explorer web browser,复习,状态单元的作用,:,构建存储（,Build memories,）,控制其他状态单元与组合逻辑间的信息流动,用,D,型翻转器（,D-flip-flops,）构建寄存器,时钟定义,D,型翻转器何时改变,建立和保持（,Setup and Hold,）时间重要,为了构建更快的时钟，可将长延时的工作流水化,有限状态机非常有用,表达状态和变化,组合逻辑,FSMs,有状态和变化,如何从一个状态变化为另一状态,?,答案,:,组合逻辑,真值表,:,唯一定义组合逻辑函数,0,关于组合逻辑，需要学些什么,?,如何设计,:,给定定义,将其分解为可管理的大小来实现,如何分析,:,延时多少,价格多少,能耗多少,具体对我们,:,用逻辑门电路来实现,（,TT,）真值表 例,#1:1,iff,one(not both),a,b,=1,a,b,y,0,0,0,0,1,1,1,0,1,1,1,0,（,TT,）真值表例,#2:2,位加法,多少行,?,TT,例,#3:32,位无符号数加法,多少行,?,TT,真值表例,#3:3-,输入多数（,majority,）电路,逻辑门,(1/2),And,vs.,Or,AND,Gate,（与门）,C,A,B,符号,定义,AN,D,逻辑门,(2/2),2,输入门扩展为,n,输入,N,输入,XOR,是唯一一个扩展方法不明显的,非常简单,:XOR=1,当且仅当其输入中,1,的个数为奇数,真值表,门,(,如多数电路,),真值表,门电路,(,如,有限状态机电路,),PS,Input,NS,Output,00,0,00,0,00,1,01,0,01,0,00,0,01,1,10,0,10,0,00,0,10,1,00,1,或者等价地,布尔代数,Boolean Algebra,George,Boole,19,世纪数学家,开发了涉及逻辑的数学系统,(,代数,),后来称为,“,布尔代数,”,基本函数,:AND,OR,和,NOT,布尔代数的重要意义在于：,由,AND,OR,和,NOT,构建的门电路和布尔代数的代数式间存在一一对应,+,即,OR,即,AND,x,即,NOT,布尔代数,(,例,“,多数”函数,),y=a b+a c+b c,y=,ab,+ac+,bc,布尔代数,(,如,有限状态机,),PS,Input,NS,Output,00,0,00,0,00,1,01,0,01,0,00,0,01,1,10,0,10,0,00,0,10,1,00,1,或者等价地,y=PS,1,PS,0,INPUT,布尔代数,:,电路化简,布尔代数也可用于,电路,证明：,如电路,X=,电路,Y?,可用布尔代数证明,!,布尔代数运算法则,布尔代数化简实例,组合逻辑的三种表示,组合逻辑表示转换,布尔表达式,转真值表,:,对右边所有变量尝试可能的值，穷举得到真值表,转逻辑门,:,用与或非门（,AND-gate/OR-gate/Inverter,）替换布尔代数中的与或非,AND/OR/NOT,运算,门电路图,转真值表,:,用所有可能的输入组合，来对电路进行测试，得到输出值,转布尔表达式,:,逆变换,真值表转布尔表达式,?,正则表示,(1/2),乘积之和,(,ORs,of,ANDs,),正则形式,(2/2),课堂测验,(,a+b,)(,a+b,)=b,N-input gates can be thought of cascaded 2-input gates.I.e.,(a,bc,d e)=a (,bc,(d e)where is one of AND,OR,XOR,NAND,You can use,NOR(s,)with clever wiring to simulate AND,OR,&NOT,ABC,1:,FFF,2:,FF,T,3:,F,T,F,4:,F,TT,5:T,FF,6:T,F,T,7:TT,F,8:TTT,(,a+b)(a+b,)=,aa+ab+ba+bb,=0+b(a+a)+b=,b+b,=b,TRUE,(next slide),You can use,NOR(s,)with clever wiring to simulate AND,OR,&NOT.,NOR(a,a,)=,a+a,=,aa,=a,Using this NOT,can we make a NOR an OR?An And?,TRUE,Peer Instruction Answer,(,a+b,)(,a+b,)=b,N-input gates can be thought of cascaded 2-input gates.I.e.,(a,bc,d e)=a (,bc,(d e)where is one of AND,OR,XOR,NAND,You can use,NOR(s,)with clever wiring to simulate AND,OR,&NOT,ABC,1:,FFF,2:,FF,T,3:,F,T,F,4:,F,TT,5:T,FF,6:T,F,T,7:TT,F,8:TTT,N-input gates can be thought of cascaded 2-input gates.I.e.,(a,bc,d e)=a (,bc,(d e)where is one of AND,OR,XOR,NAND,FALSE,Lets confirm!,CORRECT 3-input,XYZ|AND|OR|XOR|NAND,000,|,0,|,0,|,0,|1,00,1|,0,|1|1|1,0,1,0,|,0,|1|1|1,0,11|,0,|1|,0,|1,1,00,|,0,|1|1|1,1,0,1|,0,|1|,0,|1,11,0,|,0,|1|,0,|1,111|1|1|1|,0,CORRECT 2-input,YZ|AND|OR|XOR|NAND,00,|,0,|,0,|,0,|1,0,1|,0,|1|1|1,1,0,|,0,|1|1|1,11|1|1|,0,|,0,0 0 0 1,0 1 1 1,0 1 1 1,0 1 0 1,0 1 1 0,0 1 0 0,0 1 0 0,1 1 1 1,Peer Instruction Answer(B),“小结,”,有限状态机（,FSM,）非常有用,后续课程还要学,Use this table and techniques we learned to transform from 1 to another,
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