Floating point binary arithmetic question

537 Views Asked by At

I'm doing a basic class on computer architecture and we dwell into Floating Point Arithmetic, I'm not looking for someone to solve my homework, I'm actually just going through old exams and I'm kinda stuck on one exercise here.

So here it goes:

1,010010*2^(-9) - 1,000101*2^(-6)

Here's what I tried to solve this:

  1. Brought both terms to the same exponent: 1010,010*2^(-6) - 1,000101*2^(-6)
  2. Subtracted to the following result: 1001,000101*2^(-6)

The problem now is, none of this checks out with the possible answers I was given, here's an actual picture of the question and the possible answers:

Any idea on what I'm doing wrong here?

1

There are 1 best solutions below

2
On BEST ANSWER

You need to shift the comma in the other number as $2^{-6}=1000 \cdot 2^{-9}$ in base 2