Computer Logical Organization 简明教程

Digital Number System

数字系统只能理解位置数系，其中有一些符号称为数字，并且这些符号根据它们在数字中所处的位置表示不同的值。

A digital system can understand positional number system only where there are a few symbols called digits and these symbols represent different values depending on the position they occupy in the number.

使用以下方法可以确定数字中每个数字的值：

A value of each digit in a number can be determined using

The digit
The position of the digit in the number
The base of the number system (where base is defined as the total number of digits available in the number system).

Decimal Number System

我们日常生活中所使用的数字系统就是十进制数字系统。十进制数字系统基数为 10，因为其使用了 0 至 9 共 10 个数字。在十进制数字系统中，小数点左边的各个位置依次表示个位、十位、百位、千位等。

The number system that we use in our day-to-day life is the decimal number system. Decimal number system has base 10 as it uses 10 digits from 0 to 9. In decimal number system, the successive positions to the left of the decimal point represents units, tens, hundreds, thousands and so on.

每个位置都表示基数（10）的特定幂。例如，十进制数字 1234 由个位上的数字 4、十位上的数字 3、百位上的数字 2 和千位上的数字 1 组成，其值可以写成：

Each position represents a specific power of the base (10). For example, the decimal number 1234 consists of the digit 4 in the units position, 3 in the tens position, 2 in the hundreds position, and 1 in the thousands position, and its value can be written as

(1&times1000) + (2&times100) + (3&times10) + (4&timesl)
(1&times103) + (2&times102) + (3&times101)  + (4&timesl00)
1000 + 200 + 30 + 1
1234

作为一名计算机程序员或 IT 专业人士，你应对计算机中经常使用的以下数字系统有所了解。

As a computer programmer or an IT professional, you should understand the following number systems which are frequently used in computers.

S.N.

Number System & Description

*Binary Number System*Base 2. Digits used: 0, 1

*Octal Number System*Base 8. Digits used: 0 to 7

*Hexa Decimal Number System*Base 16. Digits used: 0 to 9, Letters used: A- F

Binary Number System

特性

Characteristics

Uses two digits, 0 and 1.
Also called base 2 number system
Each position in a binary number represents a 0 power of the base (2). Example: 20
Last position in a binary number represents an x power of the base (2). Example: 2x where x represents the last position - 1.

Example

二进制数字：101012

Binary Number: 101012

计算十进制当量 −

Calculating Decimal Equivalent −

Step

Binary Number

Decimal Number

Step 1

101012

1 × 24) + (0 × 23) + (1 × 22) + (0 × 21) + (1 × 2010

Step 2

101012

(16 + 0 + 4 + 0 + 1)10

Step 3

101012

2110

Note: 101012 通常写成 10101。

Note: 101012 is normally written as 10101.

Octal Number System

特性

Characteristics

Uses eight digits, 0,1,2,3,4,5,6,7.
Also called base 8 number system
Each position in an octal number represents a 0 power of the base (8). Example: 80
Last position in an octal number represents an x power of the base (8). Example: 8x where x represents the last position - 1.

Example

八进制数 − 125708

Octal Number − 125708

计算十进制当量 −

Calculating Decimal Equivalent −

Step

Octal Number

Decimal Number

Step 1

125708

1 × 84) + (2 × 83) + (5 × 82) + (7 × 81) + (0 × 8010

Step 2

125708

(4096 + 1024 + 320 + 56 + 0)10

Step 3

125708

549610

Note: 125708 通常写成 12570。

Note: 125708 is normally written as 12570.

Hexadecimal Number System

特性

Characteristics

Uses 10 digits and 6 letters, 0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F.
Letters represents numbers starting from 10. A = 10, B = 11, C = 12, D = 13, E = 14, F = 15.
Also called base 16 number system.
Each position in a hexadecimal number represents a 0 power of the base (16). Example 160.
Last position in a hexadecimal number represents an x power of the base (16). Example 16x where x represents the last position - 1.

Example −

十六进制数：19FDE16

Hexadecimal Number: 19FDE16

计算十进制当量 −

Calculating Decimal Equivalent −

Step

Hexadecimal Number

Decimal Number

Step 1

19FDE16

1 × 164) + (9 × 163) + (F × 162) + (D × 161) + (E × 16010

Step 2

19FDE16

1 × 164) + (9 × 163) + (15 × 162) + (13 × 161) + (14 × 16010

Step 3

19FDE16

(65536 + 36864 + 3840 + 208 + 14)10

Step 4

19FDE16

10646210

Note − 19FDE16 通常写为 19FDE。

Note − 19FDE16 is normally written as 19FDE.