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

At 06:58 PM 4/20/01 -0500, Joe Rigdon wrote: ... 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(a)pacbell.net