方法 1
方法 1 的 2:
按位记数法
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1
在本例中，我们将把二进制数100110112转换为十进制数。从左到右地列出2的幂。从20开始，结果为”1″。每向右移一位，就对其指数加1。列出的元素个数应等于二进制数的位数。在本例中，10011011有8位数字，因此应列出的8个元素：128, 64, 32, 16, 8, 4, 2, 1
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2
把二进制数上的每一位数字对应地写到列表下方。
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3
从右边开始，画出线条，用于把二进制数中连续的数字和其上方的2的幂连接起来。从右边开始，画一条线，把二进制数的第一个数字和2的第一个幂值连接起来。然后，画一条线，把二进制数的第二个数字和2的第二个幂值连接起来。依次类推，画出线条把每一个数字和对应的幂值连接起来。
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4
扫描二进制数中的每一位数字。如果对应的数字为1，则在线条下方写下对应的2的幂值。如果对应的数字为0，则在线条下方写下0。
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5
把线条下方的数相加。所得总和为155。这就是二进制数10011011对应的十进制数。或者写成基数下标的形式：
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6
以上方法熟悉后，你将记得2的每一个幂值，因此可以省略第1步。
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方法 2
方法 2 的 2:双倍法
1
该方法不需要使用幂运算。因此，当你通过心算转换较大的数值时，该方法更简单，因为你只需要记下部分和。
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2
从给定二进制数最左边的数字开始。对于每一位数字，你向右移动，对之前所得总和乘以2并加上当前数值。例如，把10110012转换为十进制数，我们将采用如下步骤：
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3
1011001 → 0 * 2 + 1 = 1
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4
1011001 → 1 * 2 + 0 = 2
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5
1011001 → 2 * 2 + 1 = 5
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6
1011001 → 5 * 2 + 1 = 11
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7
1011001 → 11 * 2 + 0 = 22
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8
1011001 → 22 * 2 + 0 = 44
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9
1011001 → 44 * 2 + 1 = 8910
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10
和按位记数法一样，本方法经调整后也能把基于任何基数的数转换为十进制数。在这里采用双倍法因为这里给定的数是以2为基数的。如果给定的数是基于不同的基数，则应本方法中的2换成对应的基数。例如，如果给定数是以37为基数，则你在计算时应把*2换为*37。而最终的结果则总是对应的十进制数(基数10)。 🙂
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