GATE CSE 1987 | Question: 1-vii

Question

The exponent of a floating-point number is represented in excess-$\text{N}$ code so that:

• A. The dynamic range is large.
• B. The precision is high.
• C. The smallest number is represented by all zeros.
• D. Overflow is avoided.

Answer 1

Answer : C) The smallest number is represented by all zeros.

In computer system, a floating-point number is represented as S E M, i.e. using Sign bit, Exponent bits and Mantissa bits.

The exponent can be a positive as well as a negative number. So to represent negative number we can use $1's$ complement or $2's$ complement. Better choice would be $2's$ complement.

If we use $2's$ complement system to represent exponent, then problem will arise while comparing $2$ floating point numbers. For example, if exponent of the $2$ numbers are negative then for comparing we will have to convert them into positive number.

So, to avoid this extra work, excess-N code is used so that all exponent can be represented in positive numbers, starting with $0$.

Comments

@Deepak Poonia Sir in floating point representation exponent is stored in unsigned form ??

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@Deepak Poonia sir can u plz explain this question ?

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@abir_banerjee Exponent is stored as a biased exponent. Where Biased Exponent = Actual Exponent + Excess Bias. This Excess bias has a value of $2^{n-1}-1$ for $n$-bit number.

Answer 2

If we eliminate the options then we are left with option (C).
And (C) is the correct answer because to represent the smallest number we just only need to put all 0's in the exponent field, so to get the actual exponent we need to subtract N from 0 only.

but if we use 2's complement' 1's complement/ sign magnitude we have that convert that the -ve exponent, while in Excess-N we just need to put all exponent bits as 0's.

Comments

All 0's in Exponent field is reserved in IEEE 754 format.

So can we consider this here as its not mentioned ?

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Can you elaborate these lines of Excess-N?

The smaller the N the larger the positive range and smaller the negative range..

The larger the N the smaller the positive range and larger the negative range.

 

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 Manu Thakur 

I could not understand the benefit of using Excess-N format. Can u please explain again in more detail.

Please also tell the name of book whose pic u have shared