 # 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.