BCD accuracy (was: HP 85/Rocky Mountain BASIC replacement)

From: Bob Withers <bwit_at_pobox.com>
Date: Sat Apr 21 04:21:40 2001

Nonetheless, there is a big difference between efficient use of storage and
decimal accuracy. Your last sentence sums it up perfectly, for decimal
numbers BCD is a more accurate representation.

Bob

At 09:03 PM 4/20/2001 -0700, you wrote:
>At 06:58 PM 4/20/01 -0500, Joe Rigdon wrote:
>>...For
>>one thing, HPs use BCD arithmetic instead of binary so they'll much more
>>accurate than most other machines unless they use special software.
>...
>
>I've heard this claim many times that BCD is more accurate. I'm I just
>not understanding something?
>
>Unless you are doing financial work where the fractional numbers tend to
>be inherently decimal, BCD arithmetic, for a given number of bytes of
>storage, is less accurate than binary. As a BCD byte can represent only
>100 states vs 256 for binary, you are going to lose more than one bit of
>accuracy per byte of storage. Over a typical 13 nibble mantissa, it comes
>to more than 8b wasted. Actually, it is worse than that, for a couple
>reason having to do with normalization of the numbers. Firstly, a binary
>representation can scale the mantissa to retain every bit possible,
>whereas a BCD representation has a 4b granularity on the shifting, so it
>probably wastes two more bits there. Also, IEEE floats have an implied
>MSB for normalized numbers, so you get one extra bit there. So now you're
>probably up to 11 wasted bits in a double precision (8B) BCD
>number. Perhaps you can argue back nearly two bits because the exponent
>for a BCD number doesn't have to have as many bits as for a binary number
>as each count of the exponent results in roughly four bits shifting of the
>mantissa. Still, overall, it is still 10 wasted bits.
>
>So, OK, 0.1 (base 10) can't be exactly represented in a binary format, but
>0.11111 (base 16) can't be represented exactly in an 8B BCD representation.
>
>-----
>Jim Battle == frustum_at_pacbell.net
>
>
>
Received on Sat Apr 21 2001 - 04:21:40 BST