中国科学技术大学：《数字逻辑电路》课程教学资源（讲义）数字逻辑电路学习指导（指导教师：胡新伟）.pdf_大学文库

数字逻辑电路学习指导 2020 秋数字逻辑电路 06 班目录 1 写给信息学院的学弟学妹们的一封信 ························································ 6 2 课程综述 ···························································································· 7 2.1 简介 ························································································· 7 2.2 课程特点 ··················································································· 7 2.3 学习方法 ··················································································· 8 3 第一章数制和码制 ············································································· 10 3.1 主要内容 ··················································································· 10 3.2 学习目标 ··················································································· 10 3.3 学习方法 ··················································································· 10 3.4 思考题 ······················································································ 11 3.5 经典例题 ··················································································· 12 4 第二章逻辑代数基础 ·········································································· 14 4.1 主要内容 ··················································································· 14 4.2 学习目标 ··················································································· 14 4.3 学习方法 ··················································································· 15 4.4 思考题 ······················································································ 15 4.5 经典例题 ··················································································· 17 5 第三章门电路 ··················································································· 21 5.1 主要内容 ··················································································· 21 5.2 学习目标 ··················································································· 21 5.3 学习方法 ··················································································· 22 5.4 思考题 ······················································································ 22 5.5 经典例题 ··················································································· 24 6 第四章组合逻辑电路 ·········································································· 26 6.1 主要内容 ··················································································· 26 6.2 学习目标 ··················································································· 26 6.3 学习方法 ··················································································· 26 1

数字逻辑电路学习指导 2020 秋数字逻辑电路 06 班 6.4 思考题 ······················································································ 27 6.5 经典例题 ··················································································· 29 7 第五章半导体存储电路 ······································································· 30 7.1 主要内容 ··················································································· 30 7.2 学习目标 ··················································································· 30 7.3 学习方法 ··················································································· 31 7.4 思考题 ······················································································ 31 7.5 经典例题 ··················································································· 33 8 第六章时序逻辑电路 ·········································································· 34 8.1 主要内容 ··················································································· 34 8.2 学习目标 ··················································································· 34 8.3 学习方法 ··················································································· 35 8.4 思考题 ······················································································ 36 9 第七章脉冲波形的产生和整形电路 ························································ 40 9.1 主要内容 ··················································································· 40 9.2 学习目标 ··················································································· 40 9.3 学习方法 ··················································································· 41 9.4 思考题 ······················································································ 42 10 第八章数——模和模——数转换 ························································· 45 10.1 主要内容 ·················································································· 45 10.2 学习目标 ·················································································· 45 10.3 学习方法 ·················································································· 46 10.4 思考题 ····················································································· 46 10.5 经典例题 ·················································································· 47 11 第一章至第四章经典问题综合整理 ························································· 50 11.1 无关项的概念及其在化简逻辑函数中的应用 ····································· 50 11.1.1 无关项的概念 ···································································· 50 11.1.2 约束项 ············································································· 50 11.1.3 任意项 ············································································· 51 11.1.4 无关项在化简中的应用 ························································ 52 11.2 逻辑函数不同表达形式之间的转换 ················································· 53 11.2.1 真值表转换为逻辑函数式 ····················································· 53 11.2.2 逻辑函数式转换为真值表 ····················································· 53 11.2.3 逻辑函数式转换为卡诺图 ····················································· 53 2

数字逻辑电路学习指导 2020 秋数字逻辑电路 06 班 11.2.4 波形图转换为真值表 ··························································· 54 11.3 逻辑函数式常见形式变换 ····························································· 54 11.3.1 与或式 ⇒ 与非与非式 ························································· 54 11.3.2 与或式 ⇒ 与或非式 ···························································· 54 11.3.3 与或式 ⇒ 或与式 ······························································· 55 11.3.4 与或式 ⇒ 或非或非式 ························································· 55 11.4 怎样学习第三章 ········································································· 55 11.4.1 基本电路——互补开关电路 ·················································· 55 11.4.2 一种实现方法——二极管开关电路 ········································· 56 11.4.3 一种实现方法——MOS 管基本开关电路 ································· 56 11.4.4 一种实现方法——CMOS 反相器 ··········································· 57 11.5 关于高阻态 ··············································································· 57 11.5.1 概念 ················································································ 57 11.5.2 表示方法 ·········································································· 57 11.5.3 注意事项 ·········································································· 57 11.6 可用来实现逻辑函数的常用组合逻辑电路模块 ·································· 58 11.6.1 译码器 ············································································· 58 11.6.2 数据选择器 ······································································· 58 11.6.3 加法器 ············································································· 58 11.7 组合逻辑电路分析 ······································································ 58 11.7.1 本质 ················································································ 58 11.7.2 方法 ················································································ 59 11.7.3 想法分析 ·········································································· 59 11.8 组合逻辑电路设计 ······································································ 59 11.8.1 本质 ················································································ 59 11.8.2 方法 ················································································ 59 11.8.3 注意 ················································································ 60 11.9 逻辑抽象问题 ············································································ 60 11.10 译码器、数据选择器的应用及其比较 ············································ 60 11.10.1 译码器 ··········································································· 60 11.10.2 数据选择器 ····································································· 61 11.10.3 应用 ·············································································· 61 3

数字逻辑电路学习指导 2020 秋数字逻辑电路 06 班 11.11 功能扩展专题 ·········································································· 61 11.11.1 本质 ·············································································· 61 11.11.2 “黑盒子”模型——解题方法 ············································· 61 11.11.3 以一道作业题目为例 ························································· 63 11.12 数制和码制例题补充 ································································· 65 11.12.1 十进制码和格雷码的转换 ··················································· 65 11.12.2 二进制码和 BCD 码的转换 ················································· 65 11.13 逻辑代数基础例题补充 ······························································ 66 11.13.1 异或运算和同或运算 ························································· 66 11.13.2 利用公共项实现最简逻辑函数式 ·········································· 66 11.13.3 无关项在化简中的应用 ······················································ 66 11.14 加法器的应用 ·········································································· 67 11.14.1 加法器实现加减运算 ························································· 67 11.14.2 加法器实现乘法运算 ························································· 67 11.15 有限制的功能扩展问题 ······························································ 68 12 第五章至第八章经典问题综合整理 ························································· 70 12.1 SR 锁存器的约束条件与“不定”状态的理解 ··································· 70 12.1.1 简述 ················································································ 70 12.1.2 SR 锁存器电路结构与特性表 ················································ 70 12.1.3 SR 锁存器约束条件与“不定”状态的解读 ······························ 71 12.2 触发器的逻辑功能和触发方式 ······················································· 72 12.2.1 简介 ················································································ 72 12.2.2 逻辑功能和触发方式的关系 ·················································· 72 12.2.3 关于逻辑功能 ···································································· 73 12.3 触发器的异步置位问题 ································································ 73 12.3.1 简介 ················································································ 73 12.3.2 怎么识别是同步输入还是异步输入 ········································ 73 12.3.3 只有一个 SD 或者 RD ························································· 74 12.3.4 异步输入对主从触发器如何影响 ··········································· 75 12.4 触发器的动态特性 ······································································ 75 12.4.1 简介 ················································································ 75 12.4.2 考察要求和如何学习 ··························································· 76 4

数字逻辑电路学习指导 2020 秋数字逻辑电路 06 班 12.5 时序逻辑电路分析 ······································································ 76 12.5.1 简介 ················································································ 76 12.5.2 分析方法 ·········································································· 76 12.6 常用时序逻辑电路模块 ································································ 77 12.6.1 简介 ················································································ 77 12.6.2 同步置零、置位和异步置零、置位 ········································ 77 12.6.3 关于计数器进位输出信号 ····················································· 77 12.6.4 以移位寄存器为例分析自启动问题 ········································ 78 12.7 同步时序逻辑电路设计 ································································ 81 12.7.1 简介 ················································································ 81 12.7.2 设计方法 ·········································································· 81 12.7.3 关于学习同步时序逻辑电路设计的一些小建议 ························· 83 12.8 门电路、脉冲产生与整形电路、数模转换电路 ·································· 84 12.8.1 简介 ················································································ 84 12.8.2 TTL 电路和 CMOS 电路输入悬空问题 ··································· 84 12.8.3 性能参数 ·········································································· 84 12.8.4 学习上的建议 ···································································· 85 13 期末模拟试卷 ···················································································· 86 14 致谢 ································································································ 94 5

数字逻辑电路学习指导 2020秋数字逻辑电路06班写给信息学院的学弟学妹们的一封信亲爱的信息学院的学弟学妹们你们好：我是高源，来自信息学院1702班，信息安全专业.2020年秋季学期在胡新伟老师的数字逻辑电路班级(O6班)担任课程助教. 在学习数字逻辑电路课程的时候，被这门课程中的迷人的电子学色彩所深深吸引学习中注重把握课程特点，并基于课程特点展开深入思考以求得适合自己的学习方法，这也许是我在学习这门课程的时候还算比较顺利的原因吧.也想把一些思考和心得和大家分享，希望能够帮助有需要的同学解决一些学习这门课程中遇到的困难. 有了2020年春季学期担任数理方程课程助教的经验后，这学期在开展工作时相对更加顺利一些.考虑到有一些学习方法可以分享，以及针对大家在学习这门课程时常常遇到的疑难问题做统一的整理，为了帮助大家更加顺利地完成这门课程的学习，编写了这本《数字逻辑电路学习指导》.其中经典问题综合整理主要来自于平时批改作业中的总结，以及答疑过程中从同学们的反馈中归纳整理.在此特别感谢2020秋数字逻辑电路06班的全体同学们的配合与支持. 作为信息学院的一员，深切感受到老师们的关爱，衷心感谢各位老师的教导和帮助.希望尽自己所能，为学院的教学贡献一点点力量.所以特此将这本《数字逻辑电路学习指导》献给最亲爱的信息学院. 由于个人能力有限，并且在这本学习指导中很多地方是在分享自己的理解和思考所以难免会出现一些疏漏、不妥或者错误之处.恳请阅读这本《数字逻辑电路学习指导》的同学们给予批评指正.也欢迎同学们针对我提出的一些想法和我一起交流探讨在此留下个人联系方式Email:wazs98@ustc.edu.cmQQ:2209823112. 祝愿学弟学妹们能够顺利完成数字逻辑电路课程学习，取得理想的成绩。祝愿信息学院的教学工作越来越好。信息学院1702班信息安全专业高源 2020年11月 6

2020 秋数字逻辑电路 06 班数字逻辑电路学习指导 2020 秋数字逻辑电路 06 班写给信息学院的学弟学妹们的一封信亲爱的信息学院的学弟学妹们你们好：我是高源，来自信息学院 1702 班，信息安全专业.2020 年秋季学期在胡新伟老师的数字逻辑电路班级 (06 班) 担任课程助教. 在学习数字逻辑电路课程的时候，被这门课程中的迷人的电子学色彩所深深吸引. 学习中注重把握课程特点，并基于课程特点展开深入思考以求得适合自己的学习方法，这也许是我在学习这门课程的时候还算比较顺利的原因吧. 也想把一些思考和心得和大家分享，希望能够帮助有需要的同学解决一些学习这门课程中遇到的困难. 有了 2020 年春季学期担任数理方程课程助教的经验后，这学期在开展工作时相对更加顺利一些. 考虑到有一些学习方法可以分享，以及针对大家在学习这门课程时常常遇到的疑难问题做统一的整理，为了帮助大家更加顺利地完成这门课程的学习，编写了这本《数字逻辑电路学习指导》. 其中经典问题综合整理主要来自于平时批改作业中的总结，以及答疑过程中从同学们的反馈中归纳整理. 在此特别感谢 2020 秋数字逻辑电路 06 班的全体同学们的配合与支持. 作为信息学院的一员，深切感受到老师们的关爱，衷心感谢各位老师的教导和帮助. 希望尽自己所能，为学院的教学贡献一点点力量. 所以特此将这本《数字逻辑电路学习指导》献给最亲爱的信息学院. 由于个人能力有限，并且在这本学习指导中很多地方是在分享自己的理解和思考，所以难免会出现一些疏漏、不妥或者错误之处. 恳请阅读这本《数字逻辑电路学习指导》的同学们给予批评指正. 也欢迎同学们针对我提出的一些想法和我一起交流探讨. 在此留下个人联系方式 Email：wazs98@ustc.edu.cn QQ：2209823112. 祝愿学弟学妹们能够顺利完成数字逻辑电路课程学习，取得理想的成绩. 祝愿信息学院的教学工作越来越好. 信息学院 1702 班信息安全专业高源 2020 年 11 月 6

数字逻辑电路学习指导 2020秋数字逻辑电路06班所以，基本逻辑代数理论以及组合、时序电路的分析方法和设计原则是要熟练掌握的基本理论. 但作为一个工程性的学科，在学习时不能只注重理论的学习和理解，要从其工程性角度出发来思考问题，比如，我们在学习逻辑代数部分，常常研究逻辑函数式的化简.但有时候要思考一个问题，我们真的一定要化简，或者化到最简吗？化简是我们不变的追求吗？我们选择化简逻辑函数式，实际上是为了逻辑电路实现的方便，尽量简单的逻辑函数式可以使得元器件的数量以及连线数量尽可能少，降低成本、减少布局布线所带来的寄生电感电容、减少焊接出错的可能性等等.但我们可以思考这样一个问题，在研究竞争冒险现象时，我们提到，一种消除竞争冒险的方法是修改逻辑设计，常用手段是增加冗余项那么，我们要考虑，这时，从可靠性角度来思考，是不是最简又不是最完美的追求？实际上，对于模拟电路和数字电路，或者说，对于电子学，我们要有这样一个认识.没有最好的，只有最合适的，或者说合适的才是最好的，因为有一利就有一弊.所以，在优化某一个方面时，要问自己，牺牲了什么，可以忍受吗？作为设计者，客户要求是第位的，所以我们要在各个参数设计中做权衡，达到交户要求的电路才是最好的申路 2.3学习方法在明确了课程特点的基础上，我们可以讨论学习这门课程的方法.在这里只做概述，具体学习方法详见本书各个章节内容数字电子技术基础这门课，重点就是组合和时序逻辑电路的分析和设计.逻辑代数基础部分是作为数学基础来介绍，提供分析和设计的工具.而门电路和脉冲产生整形电路部分则是提供探讨性能的理论基础和手段.模/数和数/模转换则是作为模拟和数字两部分的衔接，以形成整体的观点所以，基本来说，要熟练掌握逻辑代数基础部分的定理、公式，以及逻辑函数的表达形式及其转化.基于此，可以利用逻辑函数这一有力工具来分析和设计数字电路.学习这一部分主要是掌握基本方法，并且深入理解其中的精华.比如，一个常见问题是组合逻辑电路模块的功能扩展，实际上这就是一个组合逻辑电路的设计，只不过可以略去逻辑抽象和真值表到逻辑式的转化，而且我们要用的不是门电路，而是中规模逻辑器件.如果这样理解，可能问题就会比较清晰.我们只需要思考，我们的目标是什么，几个输入，几个输出，控制关系，我们手里有什么，几个输入，几个输出.把输入首先对应好，每片内部的关系已经有保证，两片之间的关系需要我们思考这个电路的功能来决定，最后处理输出.这样，我们就完成了这个设计任务. 对于门电路和脉冲产生整形电路，可以用模型的观点来思考.门电路的模型可以选择这一章最初介绍的基本开关电路和基本互补开关电路，思考从这个电路出发，怎样得到基本二极管电路，有什么问题怎样优化，然后怎样得到电阻负载MOS反相器，最后得到有源负载的基本MOS反相器.这样，思路可能会比较清晰.脉冲产生和整形电路 8

2020 秋数字逻辑电路 06 班数字逻辑电路学习指导 2020 秋数字逻辑电路 06 班所以，基本逻辑代数理论以及组合、时序电路的分析方法和设计原则是要熟练掌握的基本理论. 但作为一个工程性的学科，在学习时不能只注重理论的学习和理解，要从其工程性角度出发来思考问题. 比如，我们在学习逻辑代数部分，常常研究逻辑函数式的化简. 但有时候要思考一个问题，我们真的一定要化简，或者化到最简吗？化简是我们不变的追求吗？我们选择化简逻辑函数式，实际上是为了逻辑电路实现的方便，尽量简单的逻辑函数式可以使得元器件的数量以及连线数量尽可能少，降低成本、减少布局布线所带来的寄生电感电容、减少焊接出错的可能性等等. 但我们可以思考这样一个问题，在研究竞争冒险现象时，我们提到，一种消除竞争冒险的方法是修改逻辑设计，常用手段是增加冗余项. 那么，我们要考虑，这时，从可靠性角度来思考，是不是最简又不是最完美的追求? 实际上，对于模拟电路和数字电路，或者说，对于电子学，我们要有这样一个认识. 没有最好的，只有最合适的，或者说合适的才是最好的，因为有一利就有一弊. 所以，在优化某一个方面时，要问自己，牺牲了什么，可以忍受吗? 作为设计者，客户要求是第一位的，所以我们要在各个参数设计中做权衡，达到客户要求的电路才是最好的电路. 2.3 学习方法在明确了课程特点的基础上，我们可以讨论学习这门课程的方法. 在这里只做概述，具体学习方法详见本书各个章节内容. 数字电子技术基础这门课，重点就是组合和时序逻辑电路的分析和设计. 逻辑代数基础部分是作为数学基础来介绍，提供分析和设计的工具. 而门电路和脉冲产生整形电路部分则是提供探讨性能的理论基础和手段. 模/数和数/模转换则是作为模拟和数字两部分的衔接，以形成整体的观点. 所以，基本来说，要熟练掌握逻辑代数基础部分的定理、公式，以及逻辑函数的表达形式及其转化. 基于此，可以利用逻辑函数这一有力工具来分析和设计数字电路. 学习这一部分主要是掌握基本方法，并且深入理解其中的精华. 比如，一个常见问题是组合逻辑电路模块的功能扩展，实际上这就是一个组合逻辑电路的设计，只不过可以略去逻辑抽象和真值表到逻辑式的转化，而且我们要用的不是门电路，而是中规模逻辑器件. 如果这样理解，可能问题就会比较清晰. 我们只需要思考，我们的目标是什么，几个输入，几个输出，控制关系，我们手里有什么，几个输入，几个输出. 把输入首先对应好，每片内部的关系已经有保证，两片之间的关系需要我们思考这个电路的功能来决定，最后处理输出. 这样，我们就完成了这个设计任务. 对于门电路和脉冲产生整形电路，可以用模型的观点来思考. 门电路的模型可以选择这一章最初介绍的基本开关电路和基本互补开关电路，思考从这个电路出发，怎样得到基本二极管电路，有什么问题怎样优化，然后怎样得到电阻负载 MOS 反相器，最后得到有源负载的基本 MOS 反相器. 这样，思路可能会比较清晰. 脉冲产生和整形电路 8