数电第一章

( 255)10 ( 28 1)10 ( 11111111 )2
8 ones
( 253)10 ( 255 2)10 ( 11111111 10)2 ( 11111101)2
16
Why the binary system is widely used in digital equipment and computer?
the more obvious the disadvantage is .
So octal and hexadecimal systems are used in somewhere.
18
3. Octal
There are 8 symbols in octal system:
0,1, 2, 3, 4, 5, 6, 7.
ai--coefficient of ith digit
r i--weight of ith digit
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2. binary
There are 2 symbols in binary system: 0,1.
The radix is 2 (逢二进一).
The numbers 0~17 are listed in Table 1:
(分辨性和抗干扰)
The disadvantage of binary system is:
There are many bits when the number is large.
65:
2 bits in decimal, but 7 bits in binary (1000001) The larger the number is,
n zeros
Is the smallest number in (n+1) bits
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Table 1. Decimal Binary
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
0 1 10 11 100 101 110 111 1000 1001 1010 1011 1100 1101 1110 1111 10000 10001
数值计算，逻辑判断和运算，逻辑关系
3. Good reliability, accuracy, anti-interference, security, common. Digital signal can be stored and long-distance transmitted more efficiently and reliably.
1
数字电路与系统 (第2版)
王兢，戚金清，李小兵，王开宇，唐洪，高仁璟 电子工业出版社，2011
References
1. Digital Logic Circuit Analysis & Design Victor P. Nelson et.al., Prentice Hall, 1995
(数字逻辑电路分析与设计，清华大学出版社，1997，影印版 69.00元）
The radix is 8.
(326.47)8 3 82 2 81 6 80 4 81 7 82
192
16
6 0.5 0.12
(214.62)10
19
Table 1. Decimal Binary
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
Digital 1. Binary signal, 0 and 1. Simple structure in unit circuit, easy for integration;
单元电路结构简单，易于集成
2. Not only numerical calculation but also logic judgement and operation;
2. Digital Fundamentals (Seventh Edition) Thomas L. Floyd, Prentice Hall, 2000
（数字电路， 第七版，科学出版社， 2002，英文影印版75.00元）
3. Digital Design – Principles & Practices (Third Edition) John F. Wakerly, Prentice Hall, 2001
Chapter 1. Fundamentals of Digital Logic 数字逻辑基础 §1.1 Digital Logic Circuits 数字电路
An analog quantity is one having continuous values. 连续 A digital quantity is one having a discrete set of values. 分立 处理数字信号并能完成数字运算的电路系统称为数字电路 或数字系统。
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
0 1 10 11 100 101 110 111 1000 1001 1010 1011 1100 1101 1110 1111 10000 10001
20
21
22
23
24
13
There are some regularities in TABLE 1:
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1. Decimal
There are 10 symbols in decimal system: 0,1,2,3,4,5,6,7,8,9.
The radix is 10 (逢十进一). A number can be written in polynomial (多项式) form:
194.3210 1102 9 101 4 100 3 101 2 102
(数字设计– 原理与实践，第三版，高教出版社，2001，影印版49.50元）
2
数字电路与系统
•Chapter 1 Fundamentals of Digital Logic •Chapter 2 Logic Gates •Chapter 3 Logic Algebra
逻辑门电路 逻辑代数基础 组合逻辑电路 数字逻辑基础
•Chapter 4 Combinational Logic
•Chapter 5 Flip – Flop
•Chapter 7 Pulse Circuits
触发器
时序逻辑电路 脉冲波形的产生与变换 数字系统设计基础 模数与数模转换
•Chapter 6 Sequential Logic •Chapter 8 Digital System Design
1
21
22
23
……
2n
10 100 1000
10...0
n zero s
(128)10 (27 )10 (10000000) 2
7 zeros
Is the smallest number in 8 bits
(2n )10 (10...0) 2
Radix (Base)基数：The total number of digits in a number
system is called radix or base. decimal (r=10) binary (r=2)
Number systems
octal (r=8) hexadecimal (r=16)
10
Table 1. Decimal Binary
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
0 1 10 11 100 101 110 111 1000 1001 1010 1011 1100 1101 1110 1111 10000 10001
11
(11010.11) 2
可靠性, 精度, 抗干扰能力, 保密性, 通用性. 便于长期存储和远程传输.
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§1.2 Number systems 数制
Number systems and codes are often employed in computers and digital systems. Binary, octal and hexadecimal number systems are used normally in digital system. But we used to use decimal in ordinary life. So we need to know the relations of the number systems.
The Advantage Digital has certain advantages over analog in electronics applications. Digital data is more efficiently and reliably than analog data.
5
20
21
22
21-1 22-1
2
3
23-1
24
24-1
15
2
21 1 1
22 1 11
23 1 111
2 4 1 ... 1111 ...
(2n 1)10 (11...1) 2
n ones
Is the largest number in n bits
For example:
Digital Circuits
and SystemsΒιβλιοθήκη Baidu
数字电路与系统
Lecturer: Jinqing Qi Dept. Electronic Engineering, Dalian University Of Technology Email:jinqing@dlut.edu.cn Tel: 84706002-2507, Office: B-507
•Chapter 9 Digital Analog Conversions
•Chapter 10 Memory and Programmable Logic Devices
半导体存储器及可编程逻辑器件
Chapter 11 VHDL 超高速集成电路硬件描述语言
3
考试方法
• 出勤：10分 • 作业：10分 • 期末考试：80分
8
In general, any number N of radix r can be written in the polynomial form (按权展开):
n 1
N
i m
a r
i
i
n—number of integer digits m—number of fractional digits (小数)
switch on switch switch off bright light turn off conduct diode or transistor cut off exist pulse no high voltage low
17
2) Good properties of distinguish and anti-interference
The advantages of binary system are as follows: 1) Easy-to-express In computer and digital equipment, any number is expressed by a state of a circuit device or a unit.
We note that each digit locate different position, its value is different. The magnitude of a position is defined weight. 权：表示该位置的大小 The weight of each position is a power of the radix 10.
Can be written as:
1 24 1 23 0 22 1 21 0 20 1 21 1 22
=16
=26.75
+8
+2
+0.5 +0.25
There are some regularities in TABLE 1:
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Table 1. Decimal Binary