Computer system : Clarification needed

[mathmari]

We found the exponent 100111001101111, which is a 2's complement number.
Since the first bit is 1, it is negative.
We take the complement and add 1 to make it positive.
That is 011000110010000+1=011000110010001.
Now we can find the number as usual, after which we need to put a $-$ sign in front of it.

So do we have the following ? First we write all digits again next to each other :

01001110 01101111 01101001 01110100 01000001 01100011 01100001 01010110

The first digit is the sign, so 0.

The following 15 digits represent the exponent, 100111001101111, which is a 2's complement number.

Since the first bit is 1, it is negative.

We take the complement and add 1 to make it positive.

That is 011000110010000+1=011000110010001, which corresponds to $12689$, so the exponent is $-12689$, right?

So is the actual exponent is $20079-(-12689)=32768$.

Then we get the fraction, which starts with 0110.

So the fraction is $0\cdot 2^{-1} + 1\cdot 2^{-2} + 1\cdot 2^{-3} + 0\cdot 2^{-4} +\ldots \approx 0.375$

So the number is approximately $+1.375\cdot 2^{32768}$. :unsure:

 

[I like Serena]

We take the complement and add 1 to make it positive.

That is 011000110010000+1=011000110010001, which corresponds to $12689$, so the exponent is $-12689$, right?
So is the actual exponent is $20079-(-12689)=32768$.

So the number is approximately $+1.375\cdot 2^{32768}$.

The exponent is $-12689$ instead.
We could also have calculated it by subtracting $32768$ from the $20079$ you found.
Note that $32768$ is $1000000000000000$ in binary, which is 16 bits.

So the number is approximately $+1.375\cdot 2^{-12689}$.

 

[mathmari]

The exponent is $-12689$ instead.
We could also have calculated it by subtracting $32768$ from the $20079$ you found.
Note that $32768$ is $1000000000000000$ in binary, which is 16 bits.

So the number is approximately $+1.375\cdot 2^{-12689}$.

Ahh ok! I think I understood that now! Thank you very much! (Sun)