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In Single Precision floating point number when E=0  and M not equals to 0 it represents a fractional form..(BiAS=+127)

when writing the decimal form why do we right (-1)^S * (1.M) * 2^(-126) instead of  (-1)^S * (1.M) * 2^(-127)??
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@ I feel you should take it as (-1)^S * (1.M) * 2^(E-127) for single precision because this is the format prescribed by IEEE .

The actual exponent is biased by 127 to get E that is the actual value of the exponent is E − 127. This gives the range: $2^{1-127}=2^{-126} \, to \,\, 2^{254-127}=2^{127}$  .

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@ I feel you should take it as (-1)^S * (1.M) * 2^(E-127) for single precision because this is the format prescribed by IEEE .

The actual exponent is biased by 127 to get E that is the actual value of the exponent is E − 127. This gives the range: $2^{1-127}=2^{-126} \, to \,\, 2^{254-127}=2^{127}$  .

 

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