21 votes 21 votes 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 ___________ Digital Logic gate1990 digital-logic number-representation floating-point-representation fill-in-the-blanks + – makhdoom ghaya asked Nov 18, 2016 • retagged Apr 16, 2021 by Lakshman Bhaiya makhdoom ghaya 7.9k views answer comment Share Follow See all 2 Comments See all 2 2 Comments reply Anjan commented Jan 13, 2018 reply Follow Share can someone explain this? 0 votes 0 votes VIDYADHAR SHELKE 1 commented Feb 3, 2020 reply Follow Share https://gateoverflow.in/203832/gate1990-1-iv-b 1 votes 1 votes Please log in or register to add a comment.
Best answer 20 votes 20 votes 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 $=2^6-1=63.$ minal answered Aug 21, 2017 • edited Jun 28, 2018 by Arjun minal comment Share Follow See all 18 Comments See all 18 18 Comments reply Ayush Upadhyaya commented Sep 7, 2017 reply Follow Share @ sonam vyas for (a) part wouldn't the range of exponent be -63 to + 63 because in question they have said that 7 bit signed exponent. And, we usually use bias to prevent using sign bit of exponent to represent the range. Also, in (b) they have asked us to recalculate the range of exponent if bias was given so why you have assumed bias in (a) part? 2 votes 2 votes parulk commented Sep 11, 2017 reply Follow Share Since Signed data is stored in 2'complement form by default ..so range of exponent is -64 to + 63 0 votes 0 votes Sona Barman commented Oct 20, 2017 reply Follow Share Part(b) solution is is confusing and logic is not clear. 0 votes 0 votes reena_kandari commented Jan 27, 2018 reply Follow Share in part a) bias will be 64 not 63.. 1 votes 1 votes thepeeyoosh commented Jan 27, 2018 reply Follow Share @ reena_kandari why 64? 1 votes 1 votes reena_kandari commented Jan 27, 2018 reply Follow Share Since Signed data is stored in 2'complement form by default ..so range of exponent is -64 to + 63. so we take bias positive of minimum value i.e 64 to make the minimum value to 0. 2 votes 2 votes reena_kandari commented Jan 27, 2018 reply Follow Share yes we can.. $1000000$ we store exponent value as unsigned integer . what's the problem in this? 0 votes 0 votes reena_kandari commented Jan 27, 2018 reply Follow Share @peeyoosh why are you adding sign bit here. exponent and mantissa we represent as unsigned integer. rang of biased exponent is $0<=E<=127$ so the range of actual exponent value is $-64<=E<=63$. 0 votes 0 votes meghna commented Jul 30, 2018 i reshown by meghna Jul 30, 2018 reply Follow Share shouldn't it be -166 to 166-1 ?? The base of the scale factor is 16, 0 votes 0 votes Ayush Upadhyaya commented Jul 31, 2018 reply Follow Share @meghna- If you are saying for range of exponent you are wrong. Base of scale factor means say your floating point number is 1.M * $B^{e}$ where B is your base and e is your exponent. Here they are asking what range your exponent can have given it cam only be of maximum 7 bits. So for binary number you follow 1.M * $2^e$ 2 votes 2 votes jatin khachane 1 commented Nov 10, 2018 reply Follow Share @Ayush+Upadhyaya Here base is mentioned as 16 so range for unbiased exponent will come as - $-16^{^{6}} $ to $ 16^{^{6}}-1$ ?? 0 votes 0 votes jatin khachane 1 commented Nov 10, 2018 reply Follow Share @Ayush+Upadhyaya Little out of context doubt but imp i think .. say your floating point number is 1.M * B^e where B is your base and e is your exponent. Here they are asking what range your exponent can have given it cam only be of maximum 7 bits For system other than binary ..for normalization we use same 1.M * B^e?? For other system like base 10 there are digits 0-9...so what should be normalized form thee 1.M only ?? eg 23.54 (base 10) 0 votes 0 votes Manas Mishra commented Nov 11, 2018 reply Follow Share @jatin kachane as base 16 given so i think u r right 0 votes 0 votes jatin khachane 1 commented Nov 11, 2018 reply Follow Share How can you store FFFFFFF in 7 bits ??? 0 votes 0 votes Manas Mishra commented Nov 11, 2018 reply Follow Share see , its (-1)^S * 1.M * B^E , [b = base and e = exponent} .... Now in the question given that it is signed exponent , so with 7 bits in signed magnitude u can represent -63 to +63 so the range will be from -63 to +63 0 votes 0 votes CHIRAG CHAWLA commented Nov 11, 2018 reply Follow Share 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? 0 votes 0 votes Abhisek Tiwari 4 commented Jan 14, 2019 reply Follow Share "the base of scale factor is 16" any significance ? 4 votes 4 votes Akash purbia commented Jan 16, 2020 reply Follow Share IEEE format came in 1985. 0 votes 0 votes Please log in or register to add a comment.
14 votes 14 votes 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 -2n-1 to 2n-1-1 therefore exponent range is -64 to +63. B. Now scale factor is represents in excess-64 format Therefore range -2n-1 +64 to 2n-1-1 +64 Range will be 0 to127 gate-17 answered Nov 24, 2016 gate-17 comment Share Follow See all 4 Comments See all 4 4 Comments reply Arjun commented Nov 24, 2016 reply Follow Share Since the Number is signed so the range of exponent is -2n-1 to 2n-1-1 It is given that the base is "16" and not "2". 5 votes 5 votes gate-17 commented Nov 26, 2016 i edited by gate-17 Nov 26, 2016 reply Follow Share 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 ? 0 votes 0 votes Hradesh patel commented Nov 26, 2016 reply Follow Share @Arjun sir plz explain?? 1 votes 1 votes rahul sharma 5 commented Jan 4, 2017 reply Follow Share scale factor 16,plz explain? 2 votes 2 votes Please log in or register to add a comment.
3 votes 3 votes 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 . --------------------------- 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 Anup patel answered Nov 26, 2017 • edited Dec 26, 2017 by Anup patel Anup patel comment Share Follow See all 0 reply Please log in or register to add a comment.
1 votes 1 votes 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 madhav reddy answered Apr 5, 2018 madhav reddy comment Share Follow See all 0 reply Please log in or register to add a comment.