Computer Fundamentals 简明教程

Computer - Number System

当我们键入一些字母或单词时，计算机将其翻译成数字，因为计算机只能理解数字。计算机可以理解位置数字系统，其中只有几个符号称为数字，并且这些符号根据它们在数字中占据的位置表示不同的值。

When we type some letters or words, the computer translates them in numbers as computers can understand only numbers. A computer can understand the positional number system where there are only a few symbols called digits and these symbols represent different values depending on the position they occupy in the number.

可以使用以下方法确定数字中每个数字的值 −

The value of each digit in a number can be determined using −

  1. The digit

  2. The position of the digit in the number

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

Decimal Number System

我们在日常生活中使用的数字系统是十进制数字系统。十进制数字系统有 10 个基础，因为它使用了从 0 到 9 的 10 个数字。在十进制数字系统中，小数点左侧的连续位置表示个位、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 represent units, tens, hundreds, thousands, and so on.

每个位置表示基础的特定指数（10）。例如，十进制数字 1234 由个位数字 4、十位数字 3、百位数字 2 和千位数字 1 组成。它的值可以写成

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. Its value can be written as

(1 x 1000)+ (2 x 100)+ (3 x 10)+ (4 x l)
(1 x 103)+ (2 x 102)+ (3 x 101)+ (4 x l00)
1000 + 200 + 30 + 4
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.No.

Number System and Description

1

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

2

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

3

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

Binary Number System

二进制数字系统的特征如下 −

Characteristics of the binary number system are as follows −

  1. Uses two digits, 0 and 1

  2. Also called as base 2 number system

  3. Each position in a binary number represents a 0 power of the base (2). Example 20

  4. Last position in a binary number represents a 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 x 24) + (0 x 23) + (1 x 22) + (0 x 21) + (1 x 2010

Step 2

101012

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

Step 3

101012

2110

Note − 101012 通常写为 10101。

Note − 101012 is normally written as 10101.

Octal Number System

八进制数字系统的特征如下 −

Characteristics of the octal number system are as follows −

  1. Uses eight digits, 0,1,2,3,4,5,6,7

  2. Also called as base 8 number system

  3. Each position in an octal number represents a 0 power of the base (8). Example 80

  4. Last position in an octal number represents a 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 x 84) + (2 x 83) + (5 x 82) + (7 x 81) + (0 x 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

十六进制数系统的特性包括：

Characteristics of hexadecimal number system are as follows −

  1. Uses 10 digits and 6 letters, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F

  2. Letters represent the numbers starting from 10. A = 10. B = 11, C = 12, D = 13, E = 14, F = 15

  3. Also called as base 16 number system

  4. Each position in a hexadecimal number represents a 0 power of the base (16). Example, 160

  5. Last position in a hexadecimal number represents a 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

Binary Number

Decimal Number

Step 1

19FDE16

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

Step 2

19FDE16

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

Step 3

19FDE16

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

Step 4

19FDE16

10646210

Note - 19FDE16 通常写成 19FDE。

Note − 19FDE16 is normally written as 19FDE.