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+9 votes

The exponent of a floating-point number is represented in excess-N code so that:

  1. The dynamic range is large.
  2. The precision is high.
  3. The smallest number is represented by all zeros.
  4. Overflow is avoided.
asked in Digital Logic by Boss (40.2k points) | 638 views

2 Answers

+11 votes
Best answer
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 $0$.
answered by Active (4.6k points)
edited by
but how does this explanation make option (C) correct?
Dynamic range is the ratio of the maximum absolute value representable and the minimum positive (i.e., non-zero) absolute value representable.
So if the excess-N code is used still the dynamic range will remain same.
By using scaling the precision become low.
+4 votes

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.

answered by Boss (40.2k points)
edited by
All 0's in Exponent field is reserved in IEEE 754 format.

So can we consider this here as its not mentioned ?

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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