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The value denoted by 110000100111100000 ... 0 in IEEE 754. Signal precision standard in decimal is ____.

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in Single precision format , we divide the number in the following way

MSB =sign bit

next 8 bit= Exponent

Rest 23 bit =mantissa

here sign=1

exponent=10000100=132

Now we know , fo biasing we have to subtract 127 from the Exponent

real exponent=132-127(as it is in single precision)=5

mantissa=111100000 ... 0

so the number is (1.M)XE(real exponent)=1.1111000...0 X 2=111110

which is 62

now sign bit=1 , so it is negative number

answer= -62

correct me, if i am wrong

edited by
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Here we need to know :

No of sign bit = 1

No of exponent bits = 8

No of mantissa bits = 23

We know bias value = 2n-1 - 1

                              = 27 - 1

                              = 127

Hence actual exponent = Exponent field value - Bias

                                  = (1000 0100)2 - 127

                                  = 132  -  127

                                  = 5

Now in remaining 23 bits of mantissa , only leading 4 bits are 1's..

Hence we can write the number as  :  =  - (1.1111)2  *  25  [ As MSB of given number is 1 , and we know a number is -ve when MSB is 1 ]

                                                       =  - ( 1 + 1/2 + 1/4 + 1/8 + 1/16 ) * 32

                                                       =  - 62

Hence the decimal representation of given number is - 62..

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