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At it’s core, all of the information on your computer is made up of bits – or 0’s and 1’s. There’s quite a bit of interpretation that goes on between that basic binary code and the information as it is displayed on your screen.

However, you may find a time to work with data at the binary level in PHP (and many other programming languages). Here’s a quick guide to understanding binary numbers and the common operators for handling them.
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Previously, we looked at how to calculate a binomial coefficient (to find the total number of possible combinations) and an example of how to generate a list of combinations with hard-coded loops.

A function would be much more useful to us if it was flexible – if it could generate a list of combinations for any size set of numbers. We can’t do this with the hard coded loop solution, so we need to come up with a better method.
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In statistics and probability, the combination is something special. There are tons of problems that revolve around how many combinations you can get choosing a certain number of random items from a set.

We’ve developed mathematical formulas to help us determine the number of possible combinations – and therefore the possibility of getting any single combination – but how can we generate a list of the actual combinations?
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I came across this problem on the DigitalPoint forums the other day. How can we write a script to calculate the total number of random combinations in a set (i.e. the binomial coefficient), and how can we generate a list of these combinations?

Today, we’ll tackle the first part. We’ll start with a quick primer on math – what is a binomial coefficient? Then, we’ll look into the most efficient way to calculate that and get the total number of possible combinations.
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Yesterday, I wrote a short article on generating random numbers in Javascript. The Javascript random number generator is similar to C/++ – it gives you a random number from 0 to 1 and you need to make it useful.

At the suggestion of a reader (thanks Justin), I decided to go ahead and turn the general formula for this into a short helper function to generate a random number.
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I’ve been working with PHP for some time now, and I’ve become spoiled with the rand() function for generating random numbers. It’s so simple – pass a min, pass a max, and get the number you want.

While I was working on various game-related scripts this weekend, I was left wondering how to create a random number in Javascript. It’s not quite as simple as the rand() function – we’ll have to go back to the old C-style random number generation.
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