To make the "normal" binary representation comparable via CLC,
DB2 simply flipflops the sign bit.
That is:
decimal value normal representation in storage DB2 representation

2 fffe 7ffe
1 ffff 7fff
0 0000 8000
1 0001 8001
2 0002 8002
etc. etc.
this way, the binary sorting of the DB2 representation yields the same
result as the numeric value order.
With decimal values, DB2 does a similar trick; the sign halfbyte is
moved to the left of the decimal representation:
decimal value normal representation in storage DB2 representation

+123.50 000012350c f000012350
I don't know exactly, how negative decimal values are represented,
but the sign halfbyte must be lower than f (maybe zero), and the
numeric part must be inverted somehow (maybe 9s complement or
binary complement). But I'm not sure about that.
As an application developer, you don't see anything of these
conversions, because DB2 does it under the covers and moves the
result to your host variables in the normal representation, of course.
So the internal representation of DB2 is of minor interest.
Kind regards
Bernd
Am 11.07.2012 20:27, schrieb C.M.:
> I wondered about that. The values that were being discussed here looked backwards
> (signed versus unsigned) to me. Thanks for the clarification.
>
> C.
>
>
>
> Original Message
> From: C.B.
> Sent: Wednesday, July 11, 2012 10:55 AM
> To: db2l@lists.idug.org
> Subject: [DB2L]  RE: Binary number internal representation
>
> If you think integers are bad, try floating point numbers, but there is a reason they aren't what you expect.
>
> DB2 converts the values to a form that can be compared using a CLC type instruction.
> That way multiple columns of data can be combined for an index and tested
> using a minimum of instructions. When an index is built that has a column
> with a descending sequence, the integer is converted and then one's complimented.
>
> Value DB2 Value Descending
> 2 7FFE 8001
> 1 7FFF 8000
> 0 8000 7FFF
> 1 8001 7FFE
> 2 8002 7FFD
> 3 8003 7FFC
>
> It looks confusing, but once you do it enough, it isn't so bad.
>
> C.B.
>
> Original Message
> From: D.L.
> Sent: Wednesday, July 11, 2012 10:01 AM
> To: db2l@lists.idug.org
> Subject: [DB2L]  Binary number internal representation
>
> Gosh I feel a bit silly asking this but I'm looking at column values and want to
> make sure I've got the representation of my binary numbers correct. Let's use
> small integer as an example. I have a smallint on DB2 for z/OS, which I believe
> is a signed bigendian two's compliment binary number. However, the sign is
> inverted for both positive and negative numbers.
>
> For example my SMALLINT of external value 10 is internally represented as x'800A'
> and my SMALLINT of external value of 3 is internally represented as x'7FFD'
> and 10 is x'7FF6'?
>
> End Original Message
>
>
