GATE CSE 1990 | Question: 1-iv-a

Question

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 $16,$
The range of the exponent is ___________

Comments

can someone explain this?

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https://gateoverflow.in/203832/gate1990-1-iv-b

Answer 1

• PS: It is an old question and IEEE format was not there then. Currently we use IEEE format if anything is unspecified.

As given exponent bits are $7$ bits.

So, minimum it could be all $7$ bit are $0's$ and maximum it could all $1's$.

Assuming $2's$ complement representation minimum value $=-2^{6} = -64$ and maximum value $=2^6-1=63.$

Comments

PS: It is an old question and IEEE format was not there then. Currently we use IEEE format if anything is unspecified.

If it is asked after IEEE standard then what will be the Answer?

Is Biasing will get added implicitly because Biasing is Used in IEEE Standard?

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"the base of scale factor is 16" any significance ?

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IEEE format came in 1985.

Answer 2

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

Comments

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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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 ?

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@Arjun sir plz explain??

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scale factor 16,plz explain?

Answer 3

a) range of exponent

as in a) part nothing is given about bias  so bias = 27−1−1=63

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

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b)
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

Answer 4

if we consider that the exponent is expressed in 2's complement(in most of the cases it is so because sometimes we get exponent as negative number) form then the range would be -64 to 63  and regarding the bais, it would be 64 and if we take excess 64 then the range would be 0 to 127