How Does IEEE Single Precision Format Store 7 Decimal Digits?

[shuxue]

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? How this is related to the statement $2^{-23}=1.19\times10^{-7}$?

 

[phinds]

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?

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.

How this is related to the statement $2^{-23}=1.19\times10^{-7}$?

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.

 

[shuxue]

What is meant by a precision of 23 bits (mantissa) in IEEE single precision format is equivalent to approximately 7 decimal digits precision?

 

[phinds]

What is meant by a precision of 23 bits (mantissa) in IEEE single precision format is equivalent to approximately 7 decimal digits precision?

approximately, yes. It's really very easy to remember because 2**10 = 1024 = 10**3 so 2**23 ~ 10**(23/3) ~ 10**7