# Binary Math Tricks: Shifting To Divide By Ten Ain’t Easy

On small CPUs, you often don’t have a multiply or divide instruction. Of course, good programmers know that shifting right and left will multiply or divide by a power of two. But there are always cases where you need to use something that isn’t a power of two. Sometimes you can work it out for multiplication.

For example, multiplying by 10 is common when dealing with conversion between binary and decimal. But since `10n` is equal to `8n+2n`, you can express that as a bunch of left shift three times to multiply by eight, adding that value to your original value shifted left once to multiply by two.

But division is a different problem. `n/10` does not equal `n/8-n/2` or anything else simple like that. The other day a friend showed me a very convoluted snippet of code on Stack Overflow by user [realtime] that divides a number by 10 and wanted to know how it worked. It is pretty straightforward if you just stick with the math and I’ll show you what I mean in this post. Turns out the post referenced the venerable Hacker’s Delight book, which has a wealth of little tricks like this.

# Little Hex Tricks Make Little Displays A Little Easier

Depending on the device in hand and one’s temperament, bringing up a new part can be a frolic through the verdant fields of discovery or an endless slog through the grey marshes of defeat. One of the reasons we find ourselves sticking with tried and true parts we know well is that interminable process of configuration. Once a new display controller is mostly working, writing convenience functions to make it easier to use can be very satisfying, but the very first thing is figuring out how to make it do anything at all. Friend of Hackaday [Dan Hienzsch] put together a post describing how to use a particular LED controller which serves as a nice walkthrough of figuring out the right bitmath to make things work, and includes a neat trick or two.

The bulk of the post is dedicated to describing the way [Dan] went about putting together his libraries for a 7-segment display demo board he makes. At its heart the board uses the IS31FL3728 matrix driver from ISSI. We love these ISSI LED controllers because they give you many channels of control for relatively low cost, but even with their relative simplicity you still need to do some bit twiddling to light the diodes you need. [Dan]’s post talks about some strategies for making this easier like preconfigured lookup tables with convenient offsets and masking bits to control RGB LEDs.

There’s one more trick which we think is the hidden star of the show; a spreadsheet which calculates register values based on “GUI” input! Computing the bit math required to control a display can be an exercise in frustration, especially if the logical display doesn’t fit conveniently in the physical register map of the controller. A spreadsheet like this may not be particularly sexy but it gets the job done; exactly the kind of hack we’re huge fans of here. We’ve mirrored the spreadsheet so you can peek at the formulas inside, and the original Excel document is available on his blog.

# These Bit Twiddling Tricks Will Make Your Coworkers Hate You

In the embedded world, twiddling a few bits is expected behavior. Firmware is far enough down the stack that the author may care about the number of bits and bytes used, or needs to work with registers directly to make the machine dance. Usually these operations are confined to the typical shifting and masking but sometimes a problem calls for more exotic solutions. If you need to descend down these dark depths you invariably come across the classic Bit Twiddling Hacks collected by [Sean Eron Anderson]. Here be dragons.

Bit Twiddling Hacks is exactly as described; a page full of snippets and suggestions for how to perform all manner of bit math in convenient or efficient ways. To our surprise upon reading the disclaimer at the top of the page, [Sean] observes that so many people have used the contents of the page that it’s effectively all been thoroughly tested. Considering how esoteric some of the snippets are we’d love to know how the darkest corners found use.

The page contains a variety of nifty tricks. Interview content like counting set bits makes an early appearance.  There’s more esoteric content like this trick for interleaving the bits in two u16’s into a single u32, or rounding up to the next power of two by casting floats. This author has only been forced to turn to Bit Twiddling Hacks on one occasion: to sign extend the output from an unfortunately designed sensor with unusual length registers.

Next time you need to perform an operation with bitmatch, check out Bit Twiddling Hacks. Have you ever needed it in production? How did you use it? We’d love to hear about it in the comments.