《数字逻辑设计及应用教学课件：4-3卡诺图》由会员分享，可在线阅读，更多相关《数字逻辑设计及应用教学课件：4-3卡诺图（41页珍藏版）》请在金锄头文库上搜索。
1、class-exercises,1. If ， , what is the relation between the fonction F and fonction G, complement or duality? 2. (Hamlet circuit.) Complete the timing diagram and explain the function of the circuit in Figure X4.78. Where does the circuit get its name? (P236-4.61),class-exercises,2. (Hamlet circuit.)
2、 Complete the timing diagram and explain the function of the circuit in Figure X4.78. Where does the circuit get its name? (P236-4.61),The name of the circuit comes from its output equation,F = 2B OR NOT 2B.,哈姆雷特经典台词对白： To be, or not to be: that is the question: Whether it is nobler in the mind to s
3、uffer The slings and arrows of outrageous fortune, Or to take arms against a sea of troubles, And by opposing end them? 生存或毁灭, 这是个问题: 是否应默默的忍受坎坷命运之无情打击, 还是应与深如大海之无涯苦难奋然为敌, 并将其克服。 此二抉择, 究竟是哪个较崇高?,Hamlet,4.3.3 Combinational Circuit Minimization (组合电路的化简),What is the Minimization? (什么是最简?) Formula Mini
4、mization (公式法化简) Karnaugh Maps (卡诺图化简),项数最少 每项中的变量 数最少,minimization methods (P211),The minimization methods reduce the cost of a two-level AND-OR, OR-AND, NAND-NAND, or NOR-NOR circuit in three ways: 1. By minimizing the number of first-level gates. 2. By minimizing the number of inputs on each firs
5、t-level gate. 3. By minimizing the number of inputs on the second-level gate.,ExampleF = N3,N2,N1,N0(1, 2, 3, 5, 7, 11, 13),Two-level AND-OR Circuit,ExampleF = N3,N2,N1,N0(1, 2, 3, 5, 7, 11, 13),Two-level AND-OR Circuit,Notes (P211),If two product or sum terms differ only in the complementing or not
6、 of one variable, we can combine them into a single term with one less variable. So we save one gate and the remaining gate has one fewer input. WHY MINIMIZE? Minimization is an important step in both ASIC design and in design PLDs. Extra gates and gate inputs require more area in an ASIC chip, and
7、thereby increase cost .The number of gates in a PLD is fixed, so you might think that extra gates are freeand they are, until you run out of them and have to upgrade to a bigger, slower, more expensive PLD. Fortunately, most software tools for both ASIC and PLD design have a minimization program bui
8、lt in.,4.3.3 Combinational Circuit Minimization (组合电路的化简),What is the Minimization? (什么是最简?) Formula Minimization (公式法化简) Karnaugh Maps (卡诺图化简),项数最少 每项中的变量 数最少,Formula Minimization(公式法化简),并项法： 利用 AB+AB=A(B+B)=A 吸收法： 利用 A+AB=A(1+B)=A 消项法： 利用 AB+AC+BC = AB+AC 消因子法：利用 A+AB = A+B 配项法： 利用 A+A=A A+A=1,公式法
9、化简并项法,= B + CD,= A,= B ( C + C ),利 用 AB+AB=A,F1 = A(BCD) + ABCD,F2 = AB + ACD + AB + ACD,F3 = BCD + BCD + BCD + BCD,= A (BCD) + BCD ,= B ( CD + CD + CD + CD ),= B,利 用 A+AB = A,公式法化简吸收法,F1 = (AB+C)ABD + AD,= AD 1 + B() ,F2 = AB + ABC + ABD + ABCD,= AB( 1 + C + D + CD ),= AB,F3 = A + A(BC)A+(BC+D) + B
10、C,A(BC) = A + BC,= A + (A+BC) + BC,= A+BC,= AD,公式法化简消项法,Y1 = AC + AB + BC,= AC + BC,Y2 = ABCD + (A+B)E + CDE,A + B = (A+B) = (AB),= (AB)CD + (AB)E + CDE = (AB)CD + (AB)E,Y3 = AB + BC + CD + DA + AC + AC,= AB + BC + CD + DA,公式法化简消因子法,Y1 = ABCD + (ABC),= D + (ABC),Y2 = A + ACD + ABC,= A + A(CD + BC),=
11、 A + CD + BC,Y3 = AC + AD + CD,= AC + (A+C)D,= AC + (AC)D,= AC + D,= A+B+C+D,公式法化简配项法,Y1 = ABC + ABC + ABC,= ABC + ABC + ABC + ABC,= AB + BC,Y2 = AB + AB + BC + BC,= AB + AB(C+C) + BC +BC(A+A),= AB + ABC + ABC + BC + ABC + ABC,= AB,+ AC,+ BC,4.3.3 Combinational Circuit Minimization (组合电路的化简),What is
12、 the Minimization (什么是最简?) Formula Minimization (公式法化简) Karnaugh Maps (卡诺图化简),项数最少 每项中的变量 数最少,Its difficult to find terms that can be combined in a jumble of algebraic symbols. In the next subsection, well begin to explore a minimization method that is more fit for human consumption. Our starting po
13、int will be the graphical equivalent of a truth table.,Karnaugh Maps.,(P212),4.3.4 Karnaugh Maps.,What is Karnaugh Map? How to draw the Karnaugh Map? What is the minimal sum?(最小和) How to realizes a minimal sum?(如何求最小和?),Karnaugh Maps(P212),A Karnaugh map is a graphical representation of a logic func
14、tions truth table. The map for an n-input logic function is an array with 2n cells, one for each possible input combination or minterm.,characteristic (P214) There is a very important reason for this orderingeach cell corresponds to an input combination that differs from each of its immediately adja
15、cent neighbors in only one variable. 相邻两方格只有一个因子互为反变量 In general, 2i 1-cells may be combined to form a product term containing n i literals, where n is the number of variables in the function. 2i个最小项相邻可消去i个因子,Minimizing: F = A,B,C,D ( 0, 2, 3, 5, 7, 8, 10, 11, 13 ),1、填图,2、圈组 “圈”尽可能大 圈数尽可能少 方格可重复使用,3
16、、读图,F(A,B,C,D) = BD + BC + BCD + ABD,BD,BC,ABD,step,填写卡诺图 圈组：找出可以合并的最小项 组(圈)数最少、每组(圈)包含的方块数最多 方格可重复使用，但至少有一个未被其它组圈过 圈组时应从合并数最小的开始 读图：写出化简后的乘积项 消掉既能为0也能为1的变量 保留始终为0或始终为1的变量,积之和形式： 0 反变量 1 原变量,Concepts-1 ( P216),A minimal sum ( 最小和)of a logic function F(X1,Xn) is a sum-of-products expression for F such that no sum-of-products expression for F has fewer product terms, and any sum-of-products expression with the same number of product te
