UGC NET CSE | December 2014 | Part 2 | Question: 09

Question

The range of representable normalized numbers in the floating point binary fractional representation in a $32$-bit word with $1$-bit sign, $8$-bit excess $128$ biased exponent and $23$-bit mantissa is :

• A. $2^{-128}$ to $(1-2^{-23}) \times 2^{127}$
• B. $(1-2^{-23}) \times 2^{-127}$ to $2^{128}$
• C. $(1-2^{-23}) \times 2^{-127}$ to $2^{23}$
• D. $2^{-129}$ to $(1-2^{-23}) \times 2^{127}$

Comments

answer B?

---

A) is correct

Answer 1

The range of representable normalized numbers in the floating point binary fractional representation in a 32-bit word :

bais = 2^n-1 = 2^8-1 = 128

Number 1 in normalized format =  0.0000000....23times = 2^0-128 = 2^-128

Maximum Number  1111111..22 times = 0.111111...23 times = (1- 2^-23 ) * (2^255-128) = (1- 2-²³ ) * (2¹²⁷)

Comments

can u explain this what you used as exponent??

in expoment all 1' s are allowed for finding max number ?

---

you are supporting option A as correct option.

But answer is option D. Can u explain please.

After long what I think is for accepting option D as correct one. It must include sign bit in the exponent as question is asked for range of representable normalised number.

Or there exists any other reason? Please mention if anyone got it.

---

I cant understand that why the negative numbers are not included ?

Answer 2

Option D is correct.

Comments

http://www.techtud.com/multiple-choice-question/consider-ibn-system-which-allocate-32-bits

check this says A)