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Fill in the blanks:

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.

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.

+2 votes

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

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?

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

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

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

Therefore range

-2^{n-1} +64 to 2^{n-1}-1 +64

Range will be 0 to127

Since the Number is signed so the range of exponent is

-2

^{n-1 }to 2^{n-1}-1

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

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