27 bits Are Not Enough for 8-digit Accuracy

From the inequality 10^8 < 2^27, we are likely
to conclude that we can represent 8-digit decimal 
floating-point numbers accurately by 27-bit floating-point
numbers.  However, we need 28 significant 
bits to represent some 8-digit numbers accurately. 
In general, we can show that if 10^p < 2^q-1, then 
q significant bits are always enough for p-digit decimal
accuracy.  Finally, we can define a compact 
27-bit floating-point representation that will give 28
significant bits, for numbers of practical importance.

CACM February, 1967

Goldberg, I. B.

CA670208 JB February 28, 1978  2:38 PM

1634	5	1634
1634	5	1634
1634	5	1634
1783	5	1634
1843	5	1634
1634	6	1634
1634	6	1634
1783	6	1634