Test by Bikram | Digital Logic | Test 2 | Question: 25

Question

Consider a $7$-bit floating-point representation with $3$ bits for the excess-$3$ exponent and $3$ bits for the mantissa represented in normalized form.

Then $0.375_{(10)}$ will be represented in this $7$-bit representation as _______.

• A. $0010011$
• B. $0001100$
• C. $0001101$  
• D. $0001010$

Comments

#explain plz??

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@bikram sir.. explain plz?

1st bit for sign, which is 0

last three bits for mantissa, which is 011

so answer should be 0***011

where i forget here?

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Here in this question we have to represent into 7-bit floating-point representation and we use Normalized form.

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By default we use IEEE form.

Answer is  B ->  0  001 100

 

The reason why we should consider only normalised form is we only represent +-1.M*2....we don't represent number before precision point ....so it assumes 1 is represented by default.Usually in IEEE representation we consider only normalised form but if told in the question to consider non normalised form then only we shouldn't normalise it . here nothing is mention in the question.

Answer 1

Usually in IEEE representation we consider only normalised form but if told in the question to consider non normalised form then only we shouldn't normalise it .

Here in this question to represent into 7-bit floating-point representation we use Normalized form.

The reason why we should consider only normalised form is we only represent +-1.M*2 , we don't represent number before precision point ....so it assumes 1 is represented by default.

In this question you need to represent that 0.375 base 10 to that   7-bit floating-point representation only .

Comments

it is 7-bit floating-point representation not 32 bit as you think about :)

and (excess - 3 )exponent is said in question.

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i only compare them.

u have ny other valid answer on their comparision in respect of exponent (-3 and -127)(3 bit and 8 bit exponent respectively) ?

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@Bikram 

in this question, the normalized number is taken as IEEE normalized number which is implicit normalization.

but in a similar question where the range is asked for normalized number used Explicit normalisation instead of using IEEE formats.

https://gateoverflow.in/2729/gate1996-1-25