i N E ugh for 2. The Simple Case 8-])iglit k c : racy [, I~ldNNI';T'J ('~(HA)I'IEI((} :~: We can represent each of the 90 decimal integers 10, 11, .-. , 98, 99 by the equivalent 7-bit integer, with no question regarding accuracy, as follows: (/+:/,ergd /(/cog:i:: (',rope*l,+/, (/~+w,b?'id(/~:,Masa. From the inequality 1 0 ~ < 2:, 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 ~' < 2 q ', then q significant bits are always enough for p-digit decimal accuracy. Finally, we can define a compact 27-blt floating-point representation that will give 28 significant bits, for numbers of practical importance. We can represent each of the 90 decimal fractions .10, .11, . . . , .98, .99 represented by the approximate binary fraction rounded to 7 [)Faces: .10 .11 .12 . 0 0 0 1 1 0 1 . 0 0 0 1 1 1 0 . 0 0 0 1 1 1 1 . 1 1 1 1 1 0 0 , 1 1 1 1
Communications of the ACM – Association for Computing Machinery
Published: Feb 1, 1967
It’s your single place to instantly
discover and read the research
that matters to you.
Enjoy affordable access to
over 18 million articles from more than
15,000 peer-reviewed journals.
All for just $49/month
Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly
Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place.
Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals.
Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.
All the latest content is available, no embargo periods.
“Hi guys, I cannot tell you how much I love this resource. Incredible. I really believe you've hit the nail on the head with this site in regards to solving the research-purchase issue.”Daniel C.
“Whoa! It’s like Spotify but for academic articles.”@Phil_Robichaud
“I must say, @deepdyve is a fabulous solution to the independent researcher's problem of #access to #information.”@deepthiw
“My last article couldn't be possible without the platform @deepdyve that makes journal papers cheaper.”@JoseServera