Consider a floating point binary notation with 16 bits. From left to right, it consists of 1bit for the sign (0= "+"),(adsbygoogle = window.adsbygoogle || []).push({}); ebits for the exponent represented in Excess[tex]~2^{e-1}[/tex] and the remaining bits for the decimal part of the mantissa, normalized between 1 and 2 ([tex]1 \leq m <2[/tex]).

a)Calculate the minimum value [tex]e_{min}[/tex] of the exponent that allows us to write in the above notation, both the numbersr= -8147.31 and

s= [tex]0.103 \cdot 10^{-6} [/tex];

This is what I would do.

1. Calculate the order of magnitude of bothrands

2. Write a proportion knowing that [tex]2^{10} \approx 10^3[/tex] (like say 10:3= x: 4, considering 4 the result of point 1. ).

3. Find x from the above proportion and find the highest power of 2 which includes x (like say x=15, [tex] 2^3 \leq 15 \leq 2^4[/tex], I'd take [tex]2^4[/tex])

4. Calculate [tex]e_{min}[/tex]: since it's in excess [tex]2^{e-1}[/tex], I solve the equation [tex]2^4=2^{e-1} \Rightarrow e=e_{min}=4+1=5[/tex], where [tex]2^4[/tex] is the result of point 3.

Is this resoning right?

Now, when I went to calculate the order of magnitude of r and s, I got that

Ord of Magn r=[tex]10^4[/tex], better say 4.

Ord of Magn s=[tex] 10^{-5}[/tex] better say -5.

Which should I consider as a starting point, [tex] 10^4 \mbox{ or } 10^{5} [/tex] ?

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# A floating point Notation Exercise

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