MadeEasy Test Series: Digital Logic - Ieee Representation

Question

Q: The decimal number -0.329 x 2^15 is to be represented using a 16 bit floating point format without normalization as shown above. mantissa is pure fraction in sign magnitude form. Answer using rounding off is..

My Try: As it is 16 bit IEEE , so we should use  [Exponent - 63 = 15]     (coz, without normalization) which gives E = 78. 

I dont know why they grouped 3-3 bits, so even if we group them by three.. So, 4th digit should br 1 and not 5. 

(They have taken Expo - 64 = 15) why???   

Comments

@Tushar

Don't go deep in that.You are correct bias should have been 63, when we compare with ieee754 32bit format standard.

bias= 2^(expobits -1) - 1 hence 2^(7-1) -1 in above case it should come out to be 63.

Follow the IEEE 754 32 formats only don't go by this questions they trouble us and create new doubts.

I would like Arjun sir to give inputs on this .Can we get Bias like this?

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Can u plz help in this one ? https://gateoverflow.in/37650/finding-modulus-of-a-counter

Answer 1

Answer is right . When exponent is given then dont calculate .

Answer 2

its just octal convention.

Answer 3

 Without normalistion 0.329*2¹⁵ =  (0.101010000* 2¹⁴)    =  [ 1 1001110  10101000   ] 

Now for sign = 1 then start pairing 3-3 bits ;  u wil get 47250

Answer shud be 147250  .

Comments

1001110  from where this no came , can u pls tell ?