Computer Logical Organization 简明教程
Number System Conversion
转换数字从一个进制到另一个进制有许多方法或技巧。我们将演示以下内容 −
There are many methods or techniques which can be used to convert numbers from one base to another. We’ll demonstrate here the following −
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Decimal to Other Base System
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Other Base System to Decimal
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Other Base System to Non-Decimal
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Shortcut method − Binary to Octal
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Shortcut method − Octal to Binary
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Shortcut method − Binary to Hexadecimal
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Shortcut method − Hexadecimal to Binary
Decimal to Other Base System
步骤
Steps
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Step 1 − Divide the decimal number to be converted by the value of the new base.
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Step 2 − Get the remainder from Step 1 as the rightmost digit (least significant digit) of new base number.
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Step 3 − Divide the quotient of the previous divide by the new base.
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Step 4 − Record the remainder from Step 3 as the next digit (to the left) of the new base number.
重复步骤 3 和 4，从右向左取余数，直到步骤 3 中的商变成 0。
Repeat Steps 3 and 4, getting remainders from right to left, until the quotient becomes zero in Step 3.
这样得到的最后的余数就是新基数数的最高有效数字 (MSD)。
The last remainder thus obtained will be the Most Significant Digit (MSD) of the new base number.
Example −
十进制数：2910
Decimal Number: 2910
计算二进制等价——
Calculating Binary Equivalent −
Step |
Operation |
Result |
Remainder |
Step 1 |
29 / 2 |
14 |
1 |
Step 2 |
14 / 2 |
7 |
0 |
Step 3 |
7 / 2 |
3 |
1 |
Step 4 |
3 / 2 |
1 |
1 |
Step 5 |
1 / 2 |
0 |
1 |
如步骤 2 和步骤 4 中所述，余数必须按逆序排列，这样第一个余数就变成最低有效数字 (LSD)，最后一个余数就变成最高有效数字 (MSD)。
As mentioned in Steps 2 and 4, the remainders have to be arranged in the reverse order so that the first remainder becomes the Least Significant Digit (LSD) and the last remainder becomes the Most Significant Digit (MSD).
十进制数 − 2910 = 二进制数 − 111012。
Decimal Number − 2910 = Binary Number − 111012.
Other Base System to Decimal System
步骤
Steps
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Step 1 − Determine the column (positional) value of each digit (this depends on the position of the digit and the base of the number system).
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Step 2 − Multiply the obtained column values (in Step 1) by the digits in the corresponding columns.
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Step 3 − Sum the products calculated in Step 2. The total is the equivalent value in decimal.
Example
二进制数 − 111012
Binary Number − 111012
计算十进制当量 −
Calculating Decimal Equivalent −
Step |
Binary Number |
Decimal Number |
Step 1 |
111012 |
1 × 24) + (1 × 23) + (1 × 22) + (0 × 21) + (1 × 2010 |
Step 2 |
111012 |
(16 + 8 + 4 + 0 + 1)10 |
Step 3 |
111012 |
2910 |
二进制数 − 111012 = 十进制数 − 2910
Binary Number − 111012 = Decimal Number − 2910
Other Base System to Non-Decimal System
步骤
Steps
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Step 1 − Convert the original number to a decimal number (base 10).
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Step 2 − Convert the decimal number so obtained to the new base number.
Step 1 − Convert to Decimal
Step |
Octal Number |
Decimal Number |
Step 1 |
258 |
2 × 81) + (5 × 8010 |
Step 2 |
258 |
(16 + 5 )10 |
Step 3 |
258 |
2110 |
八进制数 − 258 = 十进制数 − 2110
Octal Number − 258 = Decimal Number − 2110
Step 2 − Convert Decimal to Binary
Step |
Operation |
Result |
Remainder |
Step 1 |
21 / 2 |
10 |
1 |
Step 2 |
10 / 2 |
5 |
0 |
Step 3 |
5 / 2 |
2 |
1 |
Step 4 |
2 / 2 |
1 |
0 |
Step 5 |
1 / 2 |
0 |
1 |
十进制数 − 2110 = 二进制数 − 101012
Decimal Number − 2110 = Binary Number − 101012
八进制数 − 258 = 二进制数 − 101012
Octal Number − 258 = Binary Number − 101012
Shortcut method - Binary to Octal
步骤
Steps
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Step 1 − Divide the binary digits into groups of three (starting from the right).
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Step 2 − Convert each group of three binary digits to one octal digit.
Shortcut method - Octal to Binary
步骤
Steps
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Step 1 − Convert each octal digit to a 3 digit binary number (the octal digits may be treated as decimal for this conversion).
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Step 2 − Combine all the resulting binary groups (of 3 digits each) into a single binary number.
Shortcut method - Binary to Hexadecimal
步骤
Steps
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Step 1 − Divide the binary digits into groups of four (starting from the right).
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Step 2 − Convert each group of four binary digits to one hexadecimal symbol.