Date:         Mon, 21 Nov 2011 12:31:44 -0500
Reply-To:     bbser 2009 <bbser2009@GMAIL.COM>
Sender:       "SAS(r) Discussion" <SAS-L@LISTSERV.UGA.EDU>
From:         bbser 2009 <bbser2009@GMAIL.COM>
Subject:      Re: the largest integer, numeric variable of length 3
Comments: To: Bolotin Yevgeniy <YBolotin@schools.nyc.gov>
In-Reply-To:  <01384B2401936142AF5F65E3D12402780B775B0B@EX3VS1.nyced.org>
Content-Type: text/plain; charset="us-ascii"

Thank you, Bolotin, for correcting my error. I need coffee now!

Regards, Max
(Maaxx)


-----Original Message-----
From: Bolotin Yevgeniy [mailto:YBolotin@schools.nyc.gov]
Sent: November-21-11 12:23 PM
To: bbser 2009; SAS-L@LISTSERV.UGA.EDU
Subject: RE: the largest integer, numeric variable of length 3

The reason it's 8192 and not 4096 is because it looks like the sign is
rolled into the exponent (so your real exponent is actually 10 bits?)

Also, 8192 is not the biggest number that you can store in a 3., but
merely the biggest number you can store exactly. The exponent stores the
power of 2 that you need, not the value of that power of 2, and so the
number of distinct values you can technically store is up to
0.1111111111 x (11 ^ 11111111111) in binary = (whatever) x (2^2^11) in
decimal, and not 2^11 as you said.
but of course only the most significant 12 bits of the mantissa will be
used, which is why 8193 in 3. format is still 8192




-----Original Message-----
From: SAS(r) Discussion [mailto:SAS-L@LISTSERV.UGA.EDU] On Behalf Of
bbser 2009
Sent: Monday, November 21, 2011 11:49 AM
To: SAS-L@LISTSERV.UGA.EDU
Subject: the largest integer, numeric variable of length 3

Greetings All!

Out of curiosity, I was trying to figure out why the largest integer
stored
in a numeric variable of length 3 on Windows is 8192.

First, here is a good tutorial about how SAS stores decimal numbers.
http://kipirvine.com/asm/workbook/floating_tut.htm
Back to the topic, since the length is 3, then 1 bit for the sign, 11
for
exponent, 12 for mantissa.
Thus the largest binary is
1.111111111111x(2^11) (12 successive 1's right behind the dot)
or
111111111111.1 (12 successive 1's right before the dot).

Therefore the largest binary integer should be the one represented by 12
successive 1's, which is 4095 given by this code:

11436  data _null_;
11437    do i=0 to 11;
11438      sum+2**i;
11439    end;
11440    put sum;
11441  run;

4095
NOTE: DATA statement used (Total process time):
      real time           0.01 seconds
      cpu time            0.00 seconds

What am I missing? Thank you very much!

Regards, Max
(Maaxx)