小数二进制减法

Question

I am having difficulty understanding why the following binary subtraction gives the result that it does. I keep getting a different answer. I am trying to compute 0.1-x such that x is 0.00011001100110011001100. The answer should be 0.000000000000000000000001100[1100]...(1100 keeps repeating) When i do it, I keep getting 1100 in the very beginning.

What am I not doing correctly?

Answer 1

I think that your expected answer is wrong. Here's my solution. I'll group the bits into nybbles so that it would look readable.

  0.1000 0000 0000 0000 0000 0000 <- added zero to the rightmost to fill in the nybble
- 0.0001 1001 1001 1001 1001 1000 <- added zero to the rightmost to fill in the nybble
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Get the 2's complement of 0.0001 1001 1001 1001 1001 1000 .

  1.1110 0110 0110 0110 0110 0111 (1's complement)
+ 0.0000 0000 0000 0000 0000 0001
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  1.1110 0110 0110 0110 0110 1000 (2's complement)

Add the 2's complement to 0.1 .

  0.1000 0000 0000 0000 0000 0000
+ 1.1110 0110 0110 0110 0110 1000
_________________________________
 10.0110 0110 0110 0110 0110 1000

Since the overflow is 1 , disregard it. It just signifies that the final answer is a positive number since 0.1 is larger than 0.0001 1001 1001 1001 1001 1000 . Therefore, the final answer is 0.011001100110011001101000 .