EEE.DOG-blog/source/_posts/digital-circuit.md

title	titleEN	date	categories	tags
数电期中总结	Mid-term Summary of Digital Circuits	2019-02-28	[notes]	[circuit]

{% raw %}{% endraw %} 上学期掉了魔电的坑，这学期来搞点数电小攻略掩饰一下(☆ω☆) {% raw %}{% endraw %}

{% raw %}{% endraw %} I lost the pit of magic electricity last semester. This semester, let’s make a small strategy to hide it (☆ω☆)

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1. 数制与码制

二进制运算

补码

常用补码来表示负数，以便于计算。 正数和零补码是其自身，负数的补码方法如下： 二进制减法可以通过被减数加要减数的补码来实现。 <法一>直接法 $$(N)_{COMP}=\begin{cases}N&\text{N为正数}\2^{n}-N& \text{N为负数} \end{cases}$$

符号位为零（正数）时，补码与源码相同，符号位为1（负数）时，补码为$2^{n}-N$. <法二>观察法 欲求补码，可以先找其反码。 $$(N)_{INV}=\begin{cases}N&\text{N为正数}\(2^{n}-1)-N& \text{N为负数} \end{cases}$$

即，除符号位外其他值0变1，1变0。 随后反码整体加1即可得到补码~

常用编码

DCB

即8421恒权码。DCB作为10进制显示时，须在每一个Invalid位(>9)上加6。

Signed Numbers

使用8位，最左边一位表示符号，其余7位表示数值。

期中总结

第一周 - 初识数电

• 模拟量太复杂，不符合人类思维
• 三极管MOS管等非线性器件为魔转数提供了器件基础
• 因为模电太难，所以我们要学数电 一些要点
• TTL意思是指晶体管逻辑电路，由各种三极管和电阻组成，特点是速度快
• TTL中0-0.8V为低电平，2-5V为高电平
• 二进制与十进制相互转换(整数/小数)
• LSB(Least Significant Bit)/MSB(Most S B)

第二周 - 数制

• 反码 1's Complement
• 补码 2's Complement
• 有时候二进制太长不好用，这使16进制很方便
• 16进制类似2进制的助记符，如观察1100 0101可直接写出C5
• BCD是用一个16进制表示一个10进制数
• BCD很符合人类的思维习惯，但造成极大的资源浪费
• BCD四则运算，我觉得最好转成10进制算完再转回去，反正很方便
• 计算机BCD加法采取+6进位法
• 数字储存时最左一位是符号位
• 负数使用补码来存储(栗子)
• 1字节signed数字范围-128-127
• 合理设计存储位数，小心溢出
• 二进制乘法
• 二进制除法 与十进制类似

第三周 - 逻辑门与电路封装类型

• 非门 NOT
• 与门 AND
• 或门 OR
• 非与门 NAND
• 非或门 NOR
• 异或门 XOR
• 常见有TTL和CMOS两类
• CMOS按照供压可分为3.3V和5V两类
• fan-out是指有效input个数
• propagation delay time指响应时间
• 集成电路命名，如74LS04中74指商品级，LS指种类，04为型号
• 按复杂程度分类：SSI(1-12门)，MSI(13-99门)，LSI(100-9999门)，VLSI(10000-99999)，ULSI(100000+)

第四周 - 布尔运算

• 遵循交换，结合，分配律
• 结论A+AB=A与A+~AB=A+B
• DeMorgan's Theorems ~(AB)=(~A+~B) 与 ~(A+B)=~A~B
• ~A~B为Negative AND, ~(AB)为NAND, OR同理
• SOP格式为··+··+··
• POS格式为()*()*()
• Truth Table即为将全部可能的Input和output列表

第五周 - Karnaugh Map

• Karnaugh Map来可视化逻辑门化简

第六周 - 逻辑门组合

• NAND和NOR可以组合出其它任意门
• 加法器 左位放A AND B右位放A XOR B
• 比较器 1bitA XOR B 2bit(A0 XOR B0) NOR (A1 XOR B0)
• 译码器 逻辑二进制转控制电平输出

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课件： Lecture03.pdf Lecture04.pdf

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1. Number system and code system

Binary operation

Complement

The complement is often used to represent negative numbers for easy calculation. Positive numbers and zero complement are themselves, and the complement method of negative numbers is as follows: Binary subtraction can be implemented by adding the complement of the subtracted number to the subtracted number. Direct Method $$(N)_{COMP}=\begin{cases}N&\text{N is a positive number}\2^{n}-N& \text{N is a negative number} \end{cases}$$

When the sign bit is zero (positive number), the complement is the same as the source code. When the sign bit is 1 (negative number), the complement is $2^{n}-N$. Observation Method If you want the complement, you can find the inverse first. $$(N)_{INV}=\begin{cases}N&\text{N is a positive number}\(2^{n}-1)-N& \text{N is a negative number} \end{cases}$$

That is, except for the sign bit, 0 changes to 1, and 1 changes to 0. Then add 1 to the whole complement to get the complement~

Common coding

DCB

That is, the 8421 constant weight code. When DCB is displayed as a decimal number, 6 must be added to each Invalid bit (>9).

Signed Numbers

8 bits are used, the leftmost bit represents the sign, and the remaining 7 bits represent the value.

Mid-term summary

First week-first acquaintance with digital telephony

• The analog quantity is too complicated to conform to human thinking
• Non-linear devices such as triode and MOS tube provide the device basis for the magic speed
• Because analog electricity is too difficult, we have to learn math electricity Some points
• TTL means transistor logic circuit, composed of various transistors and resistors, and is characterized by fast speed
• 0-0.8V in TTL is low level, 2-5V is high level
• Conversion between binary and decimal (integer/decimal)
• LSB(Least Significant Bit)/MSB(Most S B)

Second week-Number system

• 1's Complement
• 2's Complement
• Sometimes the binary is too long to use, which makes hexadecimal very convenient
• Hexadecimal is similar to binary mnemonic, if you observe 1100 0101, you can write C5 directly
• BCD uses a hexadecimal number to represent a decimal number
• BCD is in line with human thinking habits, but it causes a great waste of resources
• BCD four arithmetic, I think it’s best to convert to decimal and then convert it back. Anyway, it’s very convenient
• Computer BCD addition adopts +6 carry method
• When storing numbers, the leftmost digit is the sign bit
• Negative numbers are stored using one's complement (chestnut)
• 1 byte signed number range -128-127
• Reasonably design the number of storage bits and be careful of overflow
• Binary Multiplication
• Binary Division Similar to decimal

Week 3-Logic Gate and Circuit Package Type

• NOT
• AND gate
• OR gate OR
• NOT AND gate NAND
• NOR gate
• Exclusive OR gate XOR
• Commonly there are TTL and CMOS two types
• CMOS can be divided into 3.3V and 5V according to the supply voltage
• Fan-out refers to the number of valid inputs
• propagation delay time refers to response time
• IC naming, for example, 74 in 74LS04 means commodity grade, LS means type, 04 is model
• Classification by complexity: SSI (1-12 doors), MSI (13-99 doors), LSI (100-9999 doors), VLSI (10000-99999), ULSI (100000+)

Week 4-Boolean operations

• Follow the exchange, combination, and distribution laws
• Conclusion A+AB=A and A+~AB=A+B
• DeMorgan's Theorems ~(AB)=(~A+~B) and ~(A+B)=~A~B
• ~A~B is Negative AND, ~(AB) is NAND, OR is the same
• SOP format is ··+··+··
• POS format is ()*()*()
• Truth Table is a list of all possible Input and Output

Week 5-Karnaugh Map

• Karnaugh Map to visualize logic gate simplification

Week 6-Logic Gate Combination

• NAND and NOR can be combined into any other gate
• Adder put A AND B on the left bit and A XOR B on the right bit
• Comparator 1bitA XOR B 2bit(A0 XOR B0) NOR (A1 XOR B0)
• Decoder logic binary to control level output

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Courseware: Lecture03.pdf Lecture04.pdf

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