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 May 22nd, 2017, 11:53 PM #1 Banned Camp   Joined: Aug 2011 Posts: 534 Thanks: 2 Largest integer number stored and displayed. According to the Latest Central Processing unit (CPU) available on the Desktop computer,Which is the Largest integer number stored and displayed in a software application? I.e Billion,Trillion,Quadrillion etc Thanks & Regards, Prashant S Akerkar Last edited by prashantakerkar; May 22nd, 2017 at 11:56 PM.
 May 23rd, 2017, 12:03 AM #2 Senior Member     Joined: Sep 2015 From: USA Posts: 2,203 Thanks: 1157 The CPU has almost nothing to do with the largest number that can be stored and displayed by software. Simple routines can be written to store, retrieve, display, add, subtract, multiply, and divide numbers of arbitrary length up to the storage limitations of the computer at hand.
 May 23rd, 2017, 12:24 AM #3 Senior Member   Joined: Apr 2014 From: UK Posts: 892 Thanks: 328 It is trivial to create a large number such that it would be too big to display on any screen. A googolplex is a pretty big number, but by no means the largest a CPU can deal with, and it can't be displayed in any software (without using powers or other notation!) https://en.wikipedia.org/wiki/Googolplex
May 23rd, 2017, 12:43 AM   #4
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 Originally Posted by weirddave It is trivial to create a large number such that it would be too big to display on any screen. A googolplex is a pretty big number, but by no means the largest a CPU can deal with, and it can't be displayed in any software (without using powers or other notation!) https://en.wikipedia.org/wiki/Googolplex
in a single screenful sure, but software can be written to scroll through numbers of arbitrary length, or to display selected portions of the number.

Now when you get to numbers so big that they require the system to remain functioning well beyond the expected time to fail of the components in order to display the entire number well you have a problem.

 May 23rd, 2017, 09:37 AM #5 Banned Camp   Joined: Aug 2011 Posts: 534 Thanks: 2 Thanks. But in any programming language , the long integer data type is defined. Can a computer program give us the output as 1000000000000? i.e 1 Trillion. This can be represented with the Scientific or Exponential notation. The latest desktop processor is i7 Quad core. So which is the Largest integer number from a computer program output ? Thanks & Regards, Prashant S Akerkar
May 23rd, 2017, 10:24 AM   #6
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 Originally Posted by prashantakerkar Thanks. But in any programming language , the long integer data type is defined. Can a computer program give us the output as 1000000000000? i.e 1 Trillion. This can be represented with the Scientific or Exponential notation. The latest desktop processor is i7 Quad core. So which is the Largest integer number from a computer program output ? Thanks & Regards, Prashant S Akerkar
The largest number that can be represented by a particular data type is a software implementation issue, not a hardware implementation issue. There are IEEE standards which lay out how the most common data types are implemented and the biggest compilers used in industry often use those standards.

If you want to know what the largest number that can be represented using a particular data type, you need to look at the language you are using and look at the limitations of those representations. If you're talking about exact representation of integers, the biggest integer is a 64-bit integer ("Long"), which is 9223372036854775807. If you're talking about 64-bit floating point numbers, the largest number is $\displaystyle 1.7976931348623157 \times 10^{308}$.

Note... python has a "bignum" module for representing numbers using whatever memory is available. For example, if you have a 1 Gb of space free you have approx 8 billion bits available for representation, so you can technically represent numbers as large as $\displaystyle 2^{8000000000}$.

 May 23rd, 2017, 10:41 AM #7 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,512 Thanks: 2514 Math Focus: Mainly analysis and algebra Google still works: Pi - 12.1 Trillion Digits
 May 23rd, 2017, 06:35 PM #8 Senior Member   Joined: Aug 2012 Posts: 2,101 Thanks: 605 It would not be difficult to write a calculator for transfinite ordinals and cardinals. Their arithmetic is perfectly simple, although ordinal addition is not commutative. But the rules are simple and not a particularly difficult programming exercise. Any transfinite number that can be expressed at all can be expressed as a finite string of symbols from the alphabet of standard set theory. [To the limit of my knowledge. This sounds like the kind of statement that someone like Joel David Hamkins knows the counterexample to]. You could fix a maximum expression size and you'd have no trouble writing a transfinite arithmetic package. I'm actually surprised nobody's done this. Of course it's completely useless but still ... the fact is that we can represent very large numbers using pencil and paper, and we can represent these same quantities in computers. Wait, look. There's a Wolfram Alpha page for that!! Transfinite Cardinal Arithmetic with Wolfram|Alphaâ€”Wolfram|Alpha Blog And here's a sample calculation. http://www.wolframalpha.com/input/?i...+1+%2B+aleph+2 Now those are some big numbers being represented in a computer! Last edited by Maschke; May 23rd, 2017 at 06:42 PM.
May 24th, 2017, 12:23 PM   #9
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 Originally Posted by prashantakerkar According to the Latest Central Processing unit (CPU) available on the Desktop computer,Which is the Largest integer number stored and displayed in a software application? I.e Billion,Trillion,Quadrillion etc Thanks & Regards, Prashant S Akerkar
Quote:
 Originally Posted by prashantakerkar Thanks. But in any programming language , the long integer data type is defined. Can a computer program give us the output as 1000000000000? i.e 1 Trillion. This can be represented with the Scientific or Exponential notation. The latest desktop processor is i7 Quad core. So which is the Largest integer number from a computer program output ? Thanks & Regards, Prashant S Akerkar
Thank you for those thought-provoking, intellectually invigorating questions.

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