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Standard Forms of Boolean ExpressionStandard Forms of Boolean ExpressionsEach product term is a Minterm (最小项).Standardization makes the evaluation, simplification, and implementation of Boolean expressions much more systematic and easier.The Standard SOP Form++ABC ABC ABC(sum-of-product)（最小项之和）Domain of a Boolean ExpressionThe domain（域）of a Boolean expression is the set of variables contained in the expression in either complemented or uncomplemented form.Example: +AB ABC A,B,CABC CDE BCD A,B,C,D,E++A minterm is a product term that contains all of the input variables in the domain of the expression.(with each literal no more than once)Example:AB ABCDomain: A,B,C Minterm can not be broken up because it contains all of the variables.）（AB=AB C+C=ABC+ABC ABC=ABCA minterm is a product term that contains all of the input variables in the domain of the expression.(with each literal no more than once)Example:AB ABCDomain: A,B,C Minterm can not be broken up because it contains all of the variables.1 11 0 1 1 1 0 1 0 0 1 1 1 0 0 1 0 1 0 0 0 0 0 C B A ABCABCABCABCABCABCABCABCEach product term is a Minterm (最小项).Standardization makes the evaluation, simplification, and implementation of Boolean expressions much more systematic and easier.The Standard SOP Form(sum-of-product)（最小项之和）Each sum term is a Maxterm (最大项).The Standard POS Form(product-of-sum)（最大项之积）(A+B+C )(A+B+C)EX 1: Convert the Boolean expression into standard SOP form and standard POS form.+A BC =++++=++++ABC ABC ABC ABC ABCA B B C C A A BC()()()+A BC =++++++=++++=++A B C A B C A B C A B CC A BB C A B A C ()()()()()()()EX 2：Derive a standard SOP and a standard POS expression from the Truth Table.1:Find out the 1s outputs2:Express the corresponding inputs as a product term (minterm)3:Sum all the product terms that have an output oneTruth Table SOP Expression=+++F ABC ABC ABC ABC1 1 11 1 0 1 1 0 1 0 1 1 0 0 1 1 1 1 0 0 0 1 0 0 1 0 0 0 0 0 0 F C B AEX 2：Derive a standard SOP and a standard POS expression from the Truth Table.1:Find out the 0s output 2:Express the corresponding inputs as a sum term (maxterm)3:Product all the sum terms that have an output zeroTruth Table POS Expression+++++C A B C A B C ()()()()=+++F A B C A B (1 1 11 1 0 1 1 0 1 0 1 1 0 0 1 1 1 1 0 0 0 1 0 0 1 0 0 0 0 0 0 F C B AEX 2：Derive a standard SOP and a standard POS expression from the Truth Table.An SOP expression is equal to 1 only if one or more of the product terms in the expression is equal to 1.A POS expression is equal to 0 only if one or more of the sum terms in the expression is equal to 0.1 1 11 1 0 1 1 0 1 0 1 1 0 0 1 1 1 1 0 0 0 1 0 0 1 0 0 0 0 0 0 F C B A。
第十六讲 若干常用中规模组合逻辑电路-加法器※ 加法器工作原理 ※Lecture《数字电子技术基础》第十六讲 若干常用中规模组合逻辑电路-加法器█ 加法器概述两个二进制数之间的算术运算无论是加、减、乘、除， 目前在数字计算机中都是化为若干步加法运算和移位进行 的。
因此，加法器是构成算术运算器的基本单元。
目前，常用加法器分类如下：加 法 器1位加法器半加器 全加器多位加法器串行进位加法器 超前进位加法器《数字电子技术基础》第十六讲 若干常用中规模组合逻辑电路-加法器█ 1位全加器 ◆ 半加器（Half-adder）若不考虑有来自低位的进位将两个1位二进制数相加， 称为半加。
实现半加运算的电路叫做半加器。
半加器的逻辑表达式：表1 半加器的真值表 输入 A B 0 0 1 1 0 1 0 1 输出 S CO 0 1 1 0 0 0 0 1⎧ S = AB + AB = A ⊕ B ⎨ ⎩CO = AB 半加器的逻辑电路及符号：Σ《数字电子技术基础》第十六讲 若干常用中规模组合逻辑电路-加法器◆ 全加器（Full-adder）将两个多位二进制数相加时，除了最低位以外，每一位 都应考虑来自低位的进位，即将两个对应的加数和来自低位 的进位3个数相加。
这种运算称为全加，所用电路称为全加器。
表2 全加器的真值表输 入 CI A B 0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 1 1 0 1 1 1输 出 S CO 0 0 1 0 1 0 0 1 1 0 0 1 0 1 1 1⎧ ⎪S = A⋅ B⋅ CI + AB⋅ CI + AB⋅ CI + AB⋅ CI ⎨ ⎪ ⎩CO = A⋅ B + B⋅ CI + A⋅ CI⎧S = A⊕ B ⊕ CI 或⎨ ⎩CO = AB+ CI( A + B)《数字电子技术基础》第十六讲 若干常用中规模组合逻辑电路-加法器图11位全加器74LS183的逻辑图和惯用图形符号 《数字电子技术基础》第十六讲 若干常用中规模组合逻辑电路-加法器█ 1位全加器的Verilog-HDL设计⎧ S = A ⊕ B ⊕ CI 或⎨ ⎩CO = AB + CI ( A + B )and (m1,a,b), (m2,b,cin), (m3,a,cin); xor (s1,a,b), (sum,s1,cin); or (cout,m1,m2,m3); endmodule//1位全加器设计module full_add1 (a,b,cin,sum,cout); input a,b,cin; output sum,cout; wire s1,m1,m2,m3;《数字电子技术基础》第十六讲 若干常用中规模组合逻辑电路-加法器█ 多位全加器 ◆ 串行进位加法器设计思想：依次将低位全加器的进位输出端CO接到高 位全加器的进位输入端CI即可构成多位串行加法器。
