# Read e-book Numbers and Computers

Additionally, because all the used values are "unsuspicious", harmless, and platform-neutral, string-encoded numbers can travel over networks without problems. It is uncommon to find arithmetic being done on strings directly, but it is possible, and when you do it, they are just as decimal-exact as the other decimal formats decimals and BCD.

Floating point numbers represent a vast range of values, which is very useful when your don't know ahead of time what the values might be, but it's a compromise. Some languages and some libraries have other characteristics. Lisp traditionally has infinite precision integers. Cobol has calculations with fixed point decimal numbers.

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It sounds like you're describing fixed-point numbers. Bear in mind that storing the fractional part of a number in a separate location is precisely identical to creating a single space, twice as long, and storing the whole and fractional part in the two separate halves. In other words, it's identical to storing the number as an integer but simply assuming a fixed number of decimal spaces.

### programming and human factors

Normally floating-point numbers are stored using a binary variation on scientific notation because what usually matters is significant digits. Many other methods exist though. Fixed-point decimal numbers are commonly used for example for storing currency values, where accuracy is critical up to a certain whole number of decimal places but the number of required decimal digits never changes. That would be called BCD, I think you can still use it if you really want to. However it's not really worth it as:.

The short answer is that floating point was designed for scientific calculations. It can store a number with up to a specified number of significant digits, which fits closely with how precision is measured in most scientific calculations. That tends to be supported in hardware largely because scientific calculations have tended to be the ones that benefited the most from hardware support.

For one example, financial calculations are often done with other formats -- but financial software usually does little enough real calculation that even though the necessary formats are only supported in software, performance remains perfectly adequate for most financial software. Sign up to join this community. The best answers are voted up and rise to the top.

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Asked 6 years, 11 months ago. Active 6 years, 11 months ago. Viewed 14k times. SomeKittens SomeKittens 2, 5 5 gold badges 26 26 silver badges 38 38 bronze badges. Don't know how that is any more accurate. The only difference is which values that can be represented exactly. Decimal floating point which is what you're referring two, just in a more awkward representation is no more inaccurate than binary floating point. The only difference is which values can't be represented, and because we're used to the decimal system we don't notice the errors of the decimal version.

And no, neither can represent all rational and irrational numbers.

Representing Numbers and Letters with Binary: Crash Course Computer Science #4

At the end of the day, it boils down to efficiency. Computers are binary and the circuits to work with this binary representation are far less complex.

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The importance of this may be somewhat diminished today, but thre was a time when this was very significant. Also any representation you choose to store your number in a finite space on a computer will have a finite set of values it can represent and all of them will exhibit rounding errors with some inputs. The typical floating point format with Mantissa and Exponent offers a far greater range then would be possible using two integers.

Mindor Oct 2 '12 at I would highly recommend reading through some of the articles referenced in my answer to the question What causes floating point rounding errors? There are actually modes of numbers that do that. Benjamin Pollack Benjamin Pollack 1, 8 8 silver badges 15 15 bronze badges. Don't you mean four bits not bytes in the BCD paragraph? The other option is fixed point arithmetic, where an integer represents a decimal fraction if a number - e.

Awesome, didn't know that calculators did that.

There is a third option. Floating point with a decimal exponent, like how C decimal is implemented: stackoverflow. Surely bit fixed point has more precision than bit floating point, since fixed point representations do not include a mantissa. Floats will roughly give you the same precision no matter how large or small the number is while fixed point will only give you full precision if the number you wish to store fits perfectly into its range.

The amount of carried information is identical, regardless of presentation. Range and precision go hand in hand though, so on that regard fixed-point arithmetic can be more accurate in certain ranges. And avoids nasty random rounding issues, if you know the limits within which you can work with.

## What All of Your Computer's Specs Really Mean

The difference is that for fixed-point numbers, the precision as in the size of a discrete step from one number to its successor is constant, just like with integers, whereas with floats, it grows roughly linearly with absolute value - the float number 1. You have to select your number representation appropriate to the problem domain. However it's not really worth it as: You'll very rarely run into a rounding error with 64 bit floating point It makes the arithmatic complex and inefficient It wastes 6 values every 4 bits.

Inverted Llama Inverted Llama 2 2 silver badges 9 9 bronze badges. BCD math was used a lot on early 8-bit microprocessor systems; indeed, on one popular microprocessor the , addition and subtraction with BCD are just as fast per byte as with binary. Video games frequently used BCD math for score-keeping. There's no special handling for scores wrapping at 1,, points.

Or that the first computer bugs were actual insects and that most of the internet is under water? This fascinating book is filled with fascinating facts, bright, infographic illustrations, a glossary and index, and links to specially selected websites to find out more.

## Representing and manipulating data in computers

The Royal Society Young People's Book Prize aims to inspire young people to read about science and promotes the writing of excellent, accessible books for unders. Visit Usborne Quicklinks for links to websites with video clips about unlucky numbers, artificial intelligence and coding, and challenges to see if you can beat a computer at chess or how many digits of pi you can remember. Explore the Quicklinks for this book. Sign Up. Home Browse books Catalogue Science and technology Computers and coding Also in Maths books Numbers and sums things to know about numbers, computers and coding Series: things to know.

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