Question $13$: Encoding a Number in Floating$-$Point

Your professor has designed a new $10-$bit floating$-$point representation with meaning similar to that defined

by the IEEE $754$ standard.

In particular, the bits are broken up from high to low as follows:

a $4-$bit mantissa

a $1-$bit sign

a $5-$bit exponent

Is the order of the fields above the same as in the IEEE $754$ standard?

Yes

No

The value of a given bit pattern can then be calculated from the three sets of bits as follows:

$(-1{)}^{\text{s}\text{i}\text{g}\text{n}}1.($ mantissa bits $)2^{\text{e}\text{x}\text{p}\text{b}\text{i}\text{t}\text{s}-15}$

Represent the decimal number $-0\mathrm{.}70$ using your professor's floating$-$point representation. Drop$/$truncate any

bits beyond those that fit in the mantissa.

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