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所在平台: Udemy |
课程主页: https://www.udemy.com/course/exploring-number-systems-the-language-of-digital-electronics/
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**课程名称：** 探索数制系统 —— 数字电子学语言 **课程概述：** 本课程旨在深入探讨数制系统在数字电子学中的重要性，以及如何表示和处理数据。在数字系统中，数据通常以二进制（0和1）形式存在，通过电子方式处理和存储以防止噪声干扰。数字电路广泛应用于计算机等领域，它们接受二进制和十六进制数据，而我们在日常生活中则习惯使用十进制。因此，详细学习这些数制系统对于理解数字电路设计至关重要。 **课程内容亮点：** * **熟悉不同数制下的数字表示：** 了解二进制、十进制、八进制和十六进制数制的特点，重点关注“基数”（radix）在量化信息处理中的作用。涵盖整数和小数部分的表示。 * **掌握数制间的转换技巧：** 学习十进制到二进制、八进制、十六进制的转换；二进制、八进制、十六进制到十进制的转换；二进制到八进制和十六进制的转换；八进制和十六进制到二进制的转换；以及十六进制到八进制和八进制到十六进制的转换。这些转换技巧对于在特定应用中使用合适的数制表示非常有用。 * **学习二进制算术：** 讨论无符号二进制数的加法、减法、乘法和除法。深入研究带符号二进制数的表示方法及算术运算，重点关注“补码”（One's Complement and Two's Complement）表示法和运算。 * **探索各种二进制编码：** 学习用于表示数字、字母或特殊字符的二进制编码，包括BCD码（Binary-Coded Decimal）、格雷码（Gray Code）、余三码（Excess-3 Code）、ASCII码等，并讨论它们之间的转换。课程还会提及一些实际应用中需要这些转换的场景。 * **理解错误检测与纠正：** 讨论在数据远距离传输和接收过程中使用的错误检测和纠正技术。 * **提供问题解决环节：** 针对所有相关主题都包含问题解决和练习环节，以巩固学习成果。 **核心学习目标：** * 理解数字电路中使用的数制系统。 * 熟悉不同数制下的数字表示方法。 * 掌握不同数字格式（十进制、二进制、八进制、十六进制）之间的转换。 * 学习简单的二进制算术运算。 * 理解带符号数表示及运算（补码系统）。 * 学习各种二进制编码（BCD、格雷码、余三码、ASCII，以及错误检测和纠正码）。 * 掌握数制表示、转换和二进制算术的基本原理。 * 理解数制系统是包含一组有序符号（即数字）和定义了加法、乘法及其他数学运算规则的语言系统。 * 重点讨论位置数制系统，包括十进制、二进制、八进制和十六进制，并涵盖带符号和无符号二进制数的算术。
"This course is not sponsored by or affiliated with Udemy, Inc."The study of number system is important from the view point of understanding how data are represented before they can be processed by any digital system including digital computers. In a digital system, the data is usually in binary states (0 or 1) and are processed and stored electronically to prevent errors due to noise and interfering signals. Digital circuits find applications in computers which accepts data or information in binary as well as Hexadecimal, whereas in the outside world, we humans commonly use the Decimal System. So, it is highly beneficial to learn all these number systems in detail to progress smoothly to the world of Digital Circuit Design.Discovering Number Systems used in Digital Circuits.· Familiarize number representation in different number systems.· Learn the conversion between different digital formats - Decimal, Binary, octal and hexadecimal number system.· Study simple binary Arithmetic - Addition, Subtraction, Multiplication and Division of Binary Numbers.· Learn signed number representation & signed number Arithmetic - One's and Two's Complement systems.· Find different Binary Codes - BCD, Gray, Excess-3, ASCII, Error correcting and detecting codes.Understanding the principles of number representation, conversion & Binary arithmetic.A number system is a language system consisting of an ordered set of symbols called digits with rules defined for addition, multiplication, and other mathematical operations.Commonly used Number systems are, Positional Number System & Non positional Number System. The Roman Number System is an example of non-positional number system. Here we are going to discuss the positional Number system consisting of decimal, binary, octal and hexadecimal in detail. Also, we consider binary arithmetic of signed & unsigned numbers. We will be discussing various binary codes to represent the data.Overview of the course:Familiarize number representation in different number systems. The characteristics of Decimal, Binary, Octal and Hexadecimal number systems are discussed with specific remarks on the significance of radix (base) of a number system which provides the means of quantifying information for processing by digital systems. The representations of these numbers as integer as well as fractional parts are also discussed.Next, we consider the Number base conversion techniques between Decimal to Binary, Octal and Hexadecimal systems, conversions of binary, octal and Hexadecimal numbers to Decimal, Binary to octal & Hexadecimal, Octal and Hexadecimal to Binary, Hexadecimal to Octal and Octal to hexadecimal conversions. Such conversions are very helpful in using a particular representation in some specific application.The third module covers the binary arithmetic. First, we discuss addition, subtraction, multiplication and division of unsigned binary numbers, after that we will see the different representations of signed binary numbers & the binary arithmetic, concentrating more on One's and Two's complement representations and arithmetic.The last module is dedicated for discussion on various binary codes to represent the data. They may consist of numerals, Alphabets or special characters. Mainly we study BCD, Gray code, Excess-3 code, ASCII code and their conversions to other codes. Some practical applications that demand such conversions are also mentioned. Error detection and correction techniques used while transmitting and receiving data in binary form to distant destinations are also discussed. Problem solving sessions are included for all relevant topics.
