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Given the ReSy-Float number (exam WS17)

with base=4, 3 exponent bits and 2 mantissa bits (not counting hidden bit?), how can we convert it into a decimal value?

I tried the following approach, but it yields incorrect results:

edit: added original screenshot of exam

This is the Resy-float format where we do not have any hidden bit.

ß = 4^{3}-1 div 2 = 31

Exponent E = 2.4^{2} + 1.4^{1} + 3.4^{0} - 31 = 8

Mantissa M = (2.4^{1} + 3.4^{0}).4^{1-2} = 11.4^{-1}

The represented number x is +M.B^{E} = (11.4^{-1}).4^{8} = +11.4^{7}= 180224

You use 2^{3-1} -1 for the offset \beta. Since it's base 4 there should be 4^{...}.

Also note that \beta = (B^{e}-1) div 2 = (4^{3}-1) div 2 = 31