IEEE representation

Question

Consider the following IEEE-754 single precision format

1

10101010

01010100................0

value represented by above number is _________________________

Comments

Ans given
-170*2³⁶ [explained like this (-1)⁵(1.0101010)*2^170-127 ]

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I think mantissa part not correct

they have not shifted the point

rt?

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-(1.328125)*2^43 which is equivalent to

-(170)*2^36

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(1.3281)*2^43 is it ?

Answer 1

The standard value will be : 

(−1)¹ * ( 1.01010100....0) * 2^170−127

- (1.3281) * 2⁴³

Now, make it more simpler -

(-1)¹ * (10101010.00000...) * 2³⁶ (Shifting of 7 bits)

- 170 * 2³⁶

Comments

but in ieee can we do shifting according to our need?

Normalization need shifting, but not every time

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why shifting of 7 bits?

Answer 2

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