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A 32-bit floating-point number is represented by a 7-bit signed exponent, and a 24-bit fractional mantissa. The base of the scale factor is 16,

(a) The range of the exponent is ___________

(b) The range of the exponent is ___________, if the scale factor is represented in excess-64 format.
asked in Digital Logic by Veteran (43.3k points) | 730 views

3 Answers

+1 vote
Best answer

a) range of exponent

as given exponent bits are 7 bits ....

so min it could be all 7 bit are 0's and maximum it could all 1's ...

minimum number =0 , and maximum number = 127

as in a) part nothing is given about bias .. so bias = $2^{7-1}-1=63$  (nothing is given about single precision also so i used general method )

so exponent range will be 0-63 to 127-63 = - 63 to 64 .



b) minimum number = 0 , maximum number = 127 ,

as here given excess 64 so bias number is 64 ,

then range will be 0-64=-64 to (127-64=63) 63..

here in question given that base is 16 , it will get simply shifting of mantissa bit ... yes range of value is increased by large base ...(-1)s ( 0.M) 16 E-bias .

correct me if i am wrong

answered by Veteran (13.6k points)
selected by
@ sonam vyas
for (a) part
wouldn't the range of exponent be -63 to + 63 because in question they have said that 7 bit signed exponent.
And, we usually use bias to prevent using sign bit of exponent to represent the range.
Also, in (b) they have asked us to recalculate the range of exponent if bias was given
so why you have assumed bias in (a) part?
Since Signed data is stored in 2'complement form by default range of exponent is -64 to + 63
Part(b) solution is is confusing and logic is not clear.
0 votes

The given floating point number format is 

Sign bit(1) Exponent(7 bit) Mantissa(24 bit)


A. Since the Number is signed so the range of exponent is

-2n-1 to 2n-1-1 therefore exponent range is -64 to +63.

B. Now scale factor is represents in excess-64 format

Therefore range 

-2n-1  +64 to 2n-1-1 +64


Range will be 0 to127



answered by Junior (801 points)

Since the Number is signed so the range of exponent is

-2n-1 to 2n-1-1

It is given that the base is "16" and not "2".

But we store the number in binary form so range might be the same like binary for 16 scale factor ? sir plz correct me
@Arjun sir  , then what will be the correct answer ?
@Arjun sir plz explain??
scale factor 16,plz explain?
0 votes
a) range of exponent

 in a) part we will consider default base given in que i.e 16 ..
so exponent range will be (0-63)+16 to 63+16 = - 48 to 79 .


as here given excess 64 so bias number is 64 ,

then range will be -64+64=0 to (63+64)=127
So range is 0 to 127
answered by Loyal (2.7k points)

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