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Agrek11
asked
in CO and Architecture
Oct 5, 2021

569 views
2 votes

For maximum value, you need maximum possible mantissa and maximum possible exponent.

Since the exponent's maximum value that can be stored is x, but here we are using a bias of q

So, actually exponent value will be b^(x-q)

(You can relate it with the {2^(8) -1} - 127 in case of IEEE, as 2^(8) -1 maximum value (8 bits available for exponent) and 127 is the bias)

Now it is given the significant can contain P digits,

So in normalised form

Expression will look like

(1 + 1/b + 1/b^2 + 1/b^3.........)b^(x-q)

It will evaluate to

b^(x-q)(1-b^(-p))

Since the exponent's maximum value that can be stored is x, but here we are using a bias of q

So, actually exponent value will be b^(x-q)

(You can relate it with the {2^(8) -1} - 127 in case of IEEE, as 2^(8) -1 maximum value (8 bits available for exponent) and 127 is the bias)

Now it is given the significant can contain P digits,

So in normalised form

Expression will look like

(1 + 1/b + 1/b^2 + 1/b^3.........)b^(x-q)

It will evaluate to

b^(x-q)(1-b^(-p))