灰度共生矩陣及其數字特征

Any number system has a set of symbols known as Digits with some rules performing arithmetic operations. A collection of these makes a number has two parts. They are integer portion and fraction portion. These portions are separated by a point known as radix.

任何數字系統都有一組稱為數字的符號，其中某些規則執行算術運算。 這些的集合使數字分為兩個部分。 它們是整數部分和小數部分 。 這些部分被稱為radix的點隔開。

If a number has radix as 'b', then the number of numbers present in that number system will be 'b' which will range from 0 to b-1.

如果一個數字的基數為'b' ，則該數字系統中存在的數字數將為'b' ，范圍從0到b-1 。

Where,

哪里，

• N = a number

  N =一個數字

• b = radix or base to number system

  b =基數或基數系統

• n = number of digits in integer portion

  n =整數部分的位數

• m = number of digits in the fractional portion

  m =小數部分的位數

• d_n-1 = Most Significant Digit (MSD)

  d _n-1 =最高有效位(MSD)

• d_-m = Least Significant Digit (LSD)

  d _-m =最低有效位(LSD)

The commonly used number systems are:

常用的數字系統是：

Binary Number System

二進制數制

Octal Number System

八進制數字系統

Decimal Number System

小數系統

Hexadecimal Number System

十六進制數制

1)二進制數制 (1) Binary Number System)

The binary number system has its base as 2. Since b=2, it consists of two digits which range from 0 to 2-1 =1. (As discussed above, the range is from 0 to b-1).

二進制數字系統的底數為2 。 由于b = 2 ，它由兩位數字組成，范圍從0到2-1 = 1 。 (如上所述，范圍是從0到b-1 )。

Therefore, the binary number system consists of digits 0 and 1 only.

因此， 二進制數字系統僅由數字0和1組成。

Ex: (1101)2, (110101)2, (0101)2, (101.01)2, etc.

例如：(1101)2，(110101)2，(0101)2，(101.01)2等。

In Binary Number System, the portion to the left of binary point (integer part) have their weights as 2⁰, 2¹, 2² and so on from right to left. The portion on the right-hand side of the binary point (fractional part) have weights as 2^-1, 2^-2 and so on from left to right.

在二進制數字系統 ，該部分向左側二進制點(整數部分)具有它們的權重為2 ^{0，2 1，2 2}等從右到左。 二元點右側的部分(分數部分)的權重從左到右依次為2 ^{-1，2 -2} ，依此類推。

Above given binary number (101.01)₂ can be represented as:

上面給出的二進制數(101.01) ₂可以表示為：

(101.01)₂ = (1*2²) + (0*2¹) + (1*2⁰) + (0*2^-1) + (1*2^-2)

(101.01) ₂ =(1 * 2 ² )+(0 * 2 ¹ )+(1 * 2 ⁰ )+(0 * 2 ^-1 )+(1 * 2 ^-2 )

After simplifying the terms in the RHS of the equation, we will get a decimal number equivalent to binary number on the LHS which is (5.25)₁₀.

簡化方程式RHS中的項后，我們將得到一個與LHS上的二進制數等效的十進制數(5.25) ₁₀ 。

2)八進制數字系統 (2) Octal Number System)

The octal number system has its base as 8. Since b=8, it consists of eight digits which range from 0 to 8-1 =7. (As discussed above, the range is from 0 to b-1).

八進制數制的底數為8 。 由于b = 8 ，因此它由八位數字組成，范圍從0到8-1 = 7 。 (如上所述，范圍是從0到b-1 )。

It consists of digits ranging from 0 to 7 i.e., 0, 1, 2, 3, 4, 5, 6 and 7.

它由0到7之間的數字組成，即0、1、2、3、4、5、6和7 。

Ex: (73)8, (420)8, (125.13)8, etc.

例如：(73)8，(420)8，(125.13)8等

In Octal Number System the positional values/weights to the left of octal point in integer part are as 8⁰, 8¹, 8² and so on from right to left whereas the weights in the right-hand side in fractional part are as 8^-1, 8^-2 and so on from left to right.

在八進制數系統的位置值/權重為八進制點的左側在整數部分是作為8 ^{0，8 1，8 2}等從右到左，而在小數部分的右手側上的權重是作為8 ^{-1，8 -2}等等，從左到右。

Above given octal number (125.13)₈ can be represented as:

上面給出的八進制數(125.13) ₈可以表示為：

(125.13)₈ = (1*8²) + (2*8¹) + (5*8⁰) + (1*8^-1) + (3*8^-2)

(125.13) ₈ =(1 * 8 ² )+(2 * 8 ¹ )+(5 * 8 ⁰ )+(1 * 8 ^-1 )+(3 * 8 ^-2 )

After simplifying the terms in the RHS of the equation, we will get a decimal number equivalent to octal number on the LHS which is (85.140625)₁₀.

簡化方程式RHS中的項后，我們將得到一個與LHS上的八進制數等效的十進制數，即(85.140625) ₁₀ 。

小數系統 (Decimal Number System)

The Decimal Number System has its base as 10. Since b=10, it consists of 10 digits which range from 0 to 10-1 = 9. (As discussed above, the range is from 0 to b-1).

小數系統的底數為10 。 由于b = 10 ，因此它由10個數字組成，范圍從0到10-1 = 9 。 (如上所述，范圍是從0到b-1 )。

It consists of digits ranging from 0 to 9 i.e., 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9.

它由0到9之間的數字組成，即0、1、2、3、4、5、6、7、8和9 。

Ex: (101)10, (12)10, (999)10, (540.25)10, etc.

例如：(101)10，(12)10，(999)10，(540.25)10等

In the Decimal Number System the positional values/weights to the left of the decimal point in integer part are as 10⁰, 10¹, 10² and so on from right to left whereas the weights in the right-hand side in fractional part are as 10^-1, 10^-2 and so on from left to right.

在十進制系統的位置值/權重到小數點的左邊在整數部分是為10 ^{0，10 1，10 2}等從右到左，而在小數部分是在右手側的權重從左到右依次為10 ^{-1，10 -2}等。

Above given decimal number (540.25)₁₀ can be represented as:

高于給定的十進制數(540.25) ₁₀可以表示為：

(540.25)₁₀ = (5*10²) + (4*10¹) + (0*10⁰) + (2*10^-1) + (5*10^-2)

(540.25) ₁₀ =(5 * 10 ² )+(4 * 10 ¹ )+(0 * 10 ⁰ )+(2 * 10 ^-1 )+(5 * 10 ^-2 )

After simplifying the terms in the RHS of the equation, we will get a decimal number equivalent to the decimal number on the LHS.

簡化方程式RHS中的項后，我們將得到一個與LHS上的十進制數等效的十進制數。

4)十六進制數制 (4) Hexadecimal Number System)

The Hexadecimal Number System has its base as 16. Since b=16, it consists of 16 digits which range from 0 to 16-1 = 15. (As discussed above, the range is from 0 to b-1).

十六進制數字系統的底數為16 。 由于b = 16 ，它由16位數字組成，范圍從0到16-1 = 15 。 (如上所述，范圍是從0到b-1 )。

It consists of both digits and alphabets where digits range from 0 to 9 i.e., 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 and alphabets range from A to F where (A=10), (B=11), (C=12), (D=13), (E=14) and (F=15).

它由數字和字母組成，其中數字范圍從0到9，即0、1、2、3、4、5、6、7、8、9，字母范圍從A到F ，其中( A = 10) ， ( B ＝ 11) ，( C ＝ 12 )，( D ＝ 13 )，( E ＝ 14 )和( F ＝ 15 )。

Ex: (123)16, (459)16, (12A3F.12)16, etc.

例如：(123)16，(459)16，(12A3F.12)16等。

In the Hexadecimal Number System the positional values/weights to the left of the decimal point in integer part are as 16⁰, 16¹, 16² and so on from right to left whereas the weights in the right-hand side in fractional part are as 16^-1, 16^-2 and so on from left to right.

在十六進制數系統的位置值/權重到小數點的左邊在整數部分是為16 ^{0，16 1，16 2}等從右到左，而在小數部分是在右手側的權重從左到右依次為16 ^{-1，16 -2}等。

Above given Hexadecimal number (12A.13)₁₆ can be represented as:

上面給出的十六進制數(12A.13) ₁₆可以表示為：

(12A.13)₁₆ = (1*16²) + (2*16¹) + (10*16⁰) + (1*16^-1) + (3*16^-2)

(12A.13) ₁₆ =(1 * 16 ² )+(2 * 16 ¹ )+(10 * 16 ⁰ )+(1 * 16 ^-1 )+(3 * 16 ^-2 )

After simplifying the terms in the RHS of the equation, we will get a decimal number equivalent to decimal number on the LHS which is (298. 06640625)₁₀.

簡化方程式RHS中的項后，我們將得到一個與LHS上的十進制數相等的十進制數，即(298. 06640625) ₁₀ 。

翻譯自: https://www.includehelp.com/basics/number-systems-and-their-representation.aspx

灰度共生矩陣及其數字特征

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