浮点尾数偏差
有谁知道如何出去解决这个问题？
* a = 1.0 × 2^9
* b = −1.0 × 2^9
* c = 1.0 × 2^1
使用浮点（表示形式使用 14 位格式，5 位表示偏置为 16 的指数，8 位归一化尾数，单个符号位表示数字），执行以下两个计算，密切注意操作顺序。
* b + (a + c) = ?
* (b + a) + c = ?
Does anybody know how to go out solving this problem?
* a = 1.0 × 2^9
* b = −1.0 × 2^9
* c = 1.0 × 2^1
Using the floating-point (the representation uses a 14-bit format, 5 bits for the exponent with a bias of 16, a normalized mantissa of 8 bits, and a single sign bit for the number), perform the following two calculations, paying close attention to the order of operations.
* b + (a + c) = ?
* (b + a) + c = ?
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要完成此练习，您只需按照添加步骤进行操作，如下所示：
http://en.wikipedia.org/wiki/Floating_point#Addition_and_subtraction
To go through this exercise, you just follow the addition steps, as explained e.g. there:
http://en.wikipedia.org/wiki/Floating_point#Addition_and_subtraction
如果我做对了，看起来你不能将 c 反规范化为 a 的指数，所以你最终会用相同的指数将 1 加到 -1 上，所以你最终会得到 0。我相信这是一个关于以浮点格式将小数加到大数的局限性。
我将把第二个问题留给你......
If I'm doing this right, it looks like you can't denormalize c to a's exponent, so you end up adding 1 to -1 with the same exponent, and so you end up with 0. I believe this is a lesson on the limitations of adding a small number to a large one in a floating point format.
I will leave the second problem to you...