The discussion revolves around how IEEE single precision format represents numbers, specifically focusing on its ability to store approximately 7 decimal digits. Participants explore the relationship between the binary representation and decimal precision, particularly in relation to the mathematical statement ##2^{-23}=1.19\times10^{-7}##.
Participants express similar inquiries regarding the precision of the IEEE format, but there is no consensus on the clarity of the examples or explanations provided. Some points are reiterated, indicating a lack of resolution on certain aspects of the discussion.
Participants reference the relationship between binary and decimal representations, but the discussion does not resolve the underlying assumptions about the precision and its implications in practical applications.
Have you done any research on your own to understand that format? It's very common and it should be easy to find examples already posted on the internet, if not in your textbook.shuxue said:Could someone please show me some examples how IEEE single precision format can used to store approximately 7 decimal digits of a number when the number is written in decimal format?
that's just a radix conversion. It's relevance to the IEEE format is that you only have a 23 bit explicit mantissa so that's the smallest number body (apart from exponent) you can express in that format. It will all be clear once you have studied the format.How this is related to the statement ##2^{-23}=1.19\times10^{-7}##?
approximately, yes. It's really very easy to remember because 2**10 = 1024 = 10**3 so 2**23 ~ 10**(23/3) ~ 10**7shuxue said:What is meant by a precision of 23 bits (mantissa) in IEEE single precision format is equivalent to approximately 7 decimal digits precision?