Computer Fundamentals 简明教程
Computer - Number Conversion
有许多方法或技术可用于将数字从一个基数转换为另一个基数。在本章中，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. In this chapter, we’ll demonstrate 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
Step 1 ——将要转换的十进制数除以新基数。
Step 1 − Divide the decimal number to be converted by the value of the new base.
Step 2 ——将步骤 1 中的余数作为新基数数的右数最末位数字（最低有效数字）。
Step 2 − Get the remainder from Step 1 as the rightmost digit (least significant digit) of the new base number.
Step 3 ——将前一次除法的商再除以新基数。
Step 3 − Divide the quotient of the previous divide by the new base.
Step 4 ——将步骤 3 中的余数记录为新基数数的下一个数字（向左）。
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
Step 1 ——确定每个数字的列（位置）值（这取决于数字的位置和数制系统的基数）。
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).
Step 2 ——将步骤 1 中得到的列值与位于相应列中的数字相乘。
Step 2 − Multiply the obtained column values (in Step 1) by the digits in the corresponding columns.
Step 3 − 计算第 2 步中所得乘积之和。和数即为十进制等值。
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 x 24) + (1 x 23) + (1 x 22) + (0 x 21) + (1 x 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
Step 1 − 将原始数字转换为十进制数（以 10 为基）。
Step 1 − Convert the original number to a decimal number (base 10).
Step 2 − 将获得的十进制数转换为新的基数。
Step 2 − Convert the decimal number so obtained to the new base number.
Shortcut Method ─ Binary to Octal
Step 1 − 将二进制位分组为三组（从右侧开始）。
Step 1 − Divide the binary digits into groups of three (starting from the right).
Step 2 − 将每组三个二进制位转换为一位八进制数字。
Step 2 − Convert each group of three binary digits to one octal digit.
Shortcut Method ─ Octal to Binary
Step 1 − 将每个八进制数字转换为一位三位二进制数（在进行该转换时，可将八进制数字视为十进制数字）。
Step 1 − Convert each octal digit to a 3-digit binary number (the octal digits may be treated as decimal for this conversion).
Step 2 − 将所有所得二进制组（每组 3 位）合并为一个二进制数。
Step 2 − Combine all the resulting binary groups (of 3 digits each) into a single binary number.
Shortcut Method ─ Binary to Hexadecimal
Step 1 − 将二进制数字分为四组（从右开始）。
Step 1 − Divide the binary digits into groups of four (starting from the right).
Step 2 − 将每组四个二进制数字转换为一个十六进制符号。
Step 2 − Convert each group of four binary digits to one hexadecimal symbol.
Shortcut Method - Hexadecimal to Binary
Step 1 − 将每个十六进制数字转换为一个四位二进制数（在此转换中，十六进制数字可视为十进制数字）。
Step 1 − Convert each hexadecimal digit to a 4-digit binary number (the hexadecimal digits may be treated as decimal for this conversion).
Step 2 − 将所有结果二进制组（每组 4 位）组合成一个二进制数。
Step 2 − Combine all the resulting binary groups (of 4 digits each) into a single binary number.