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

From: Jim Battle <frustum_at_pacbell.net>
Date: Fri Apr 20 23:03:04 2001

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 Fri Apr 20 2001 - 23:03:04 BST