数字电路与系统第一章

1.4 (1, 2, 3) 1.5 (1, 3) 1.6

1.10 (1, 3, 5) 1.12 (2, 4)1.14

1.16

1.17 (1,3) 1.19 (1, 3, 5)

Homeworks (第三版):

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Chapter 1. Number systems and codes

第一章. 数制与编码

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Content 本章内容：

1. Number systems and their conversions 数制及其相互转换

2. BCD and Grey codes BCD和格雷码

3. Signed binaries 带符号的二进制数

Extended learning

Information theory and coding 信息论与编码

Content 本章内容：

1. Number systems and their conversions 数制及其相互转换

2. BCD and Grey codes BCD 和格雷码

3. Signed binaries 带符号的二进制数

Extended learning Information theory and coding 信息论与编码

Therefore, in a general sense, information is

Knowledge communicated or received

concerning a particular fact or circumstance or rather, information is an answer to a question. Information cannot be predicted and resolves uncertainty.

§1.2 Number systems 数制

1.A number system consists of an ordered set of digits, with relationship

defined for addition, substraction, multiplication, and division. 定义了加、减、乘、除关系，并按照一定顺序进行排列的数字集合称为数制。

2.Instead of decimal used in ordinary life, binary, octal and hexadecimal

are more commonly used in digital systems. 同生活中常用十进制数不同，数字系统中更常用的数制是二进制、八进制和十六进制。

3.The radix (r), or base, of the number system is the total number of

digits allowed. 数字的总个数称为数制的基数：

Number systems decimal (r =10)

binary (r =2)

octal (r =8)

hexadecimal (r =16)

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1. Decimal 十进制

●Ten symbols in decimal system ：0, 1, 2, 3, 4, 5, 6, 7, 8, 9. The radix is 10. 十进制包含十个数码，基数为10（逢十进一）。●Digits are located at different positions, the values of which are different. The value of a position is defined as the weight . 权：表示该位置的大小。●The weight of each position in the decimal system is a power of radix 10。十进制中每一个位置对应的权都是其基数10的幂。●A number can be written in polynomial (多项式) form ：

()=1032.1942

101×1

109×+0

104×+1

10

3−×+2

10

2−×+

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--weight of the digit

第i 个数字的权值--The digit

第i 个数字In general, any number N of radix r can be written in the polynomial form (按权展开):

1101,...,,,...,.n m

N a a a

a

a −−−=n --number of integer digits 整数部分的位数i a th i i

r m --number of fractional digits 小数部分的位数

th i 1

n i

i

i m

a r −=−= Integer digits Radix point Fractional digits

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2. Binary 二进制

●Two symbols in a binary system ：0, 1. The radix is 2. 二进制包含两个数字，基数为2（逢二进一）。●The weights in the binary system are powers of radix 2。二进制权值都是基数2的幂。●A number can be written in polynomial (多项式) form ：

()211010.11=4

12

×202+×112+×0

02

+×2

12

−+×26.75

=312+×112−+×