numbers

3 Articles

Multi-Divi book with hand thumbing through it

Math, Optimized: Sweden’s Maximal Multi-Divi

March 28, 2025 by 30 Comments

Back in the early 1900s, before calculators lived in our pockets, crunching numbers was painstaking work. Adding machines existed, but they weren’t exactly convenient nor cheap. Enter Wilken Wilkenson and his Maximal Multi-Divi, a massive multiplication and division table that turned math into an industrialized process. Originally published in Sweden in the 1910’s, and refined over decades, his book was more than a reference. It was a modular calculating instrument, optimized for speed and efficiency. In this video, [Chris Staecker] tells all about this fascinating relic.

What makes the Multi-Divi special isn’t just its sheer size – handling up to 9995 × 995 multiplications – but its clever design. Wilkenson formatted the book like a machine, with modular sections that could be swapped out for different models. If you needed an expanded range, you could just swap in an extra 200 pages. To sell it internationally, just replace the insert – no translation needed. The book itself contains zero words, only numbers. Even the marketing pushed this as a serious calculating device, rather than just another dusty math bible.

While pinwheel machines and comptometers were available at the time, they required training and upkeep. The Multi-Divi, in contrast, required zero learning curve – just look up the numbers for instant result. And it wasn’t just multiplication: the book also handled division in reverse, plus compound interest, square roots, and even amortizations. Wilkenson effectively created a pre-digital computing tool, a kind of pocket calculator on steroids (if pockets were the size of briefcases).

Of course, no self-respecting hacker would take claims of ‘the greatest invention ever’ at face value. Wilkenson’s marketing, while grandiose, wasn’t entirely wrong – the Multi-Divi outpaced mechanical calculators in speed tests. And if you’re feeling adventurous, [Chris] has scanned the entire book, so you can try it yourself.

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Count To F Easily With This DIY Calculator

September 6, 2018 by 6 Comments

Some of the greatest electronic calculators of all time, including the venerable HP-16C, included functionality to convert numbers between different bases. 3735928559 might not mean much in base 10, but convert that to hex, and you’ll offend vegetarians. If the great calculators of yore had a way to convert between number bases, that means someone must make a standalone device to do the same, right? That’s what [leumasyerrp] is doing for their entry into the Hackaday Prize, anyway.

The Base Convert project is a simple desktop calculator designed to convert between hexadecimal, decimal, and binary. To do this, there’s an 8×8 key matrix for the numbers 0 through F. There are sixteen single LEDs, four seven-segment LEDs for the hex display, and six seven-segment LEDs for the decimal display.

While this is really just a project [leumasyerrp] came up with to learn the MSP430 microcontroller, this looks like a fantastic project given it’s great use of milled PCB for a front panel, careful selection of standoff height, and everything is tucked away into a package that looks about as professional as you can expect from a device made entirely from PCBs. Of course, the Base Convert calculator works as expected, and can easily change between number bases.

Sometimes it’s not about building the hardest or most complex project, but instead simply putting the most amount of polish into a simple project. This is a project that does that well, and we’re happy to have this in the running for the Hackaday Prize.

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Learn To Count In Seximal, A Position Above The Rest

July 20, 2018 by 42 Comments

Believe it or not, counting is not special. Quite a few animals have figured it out over the years. Tiny honeybees compare what is less and what is more, and their brains are smaller than a pinky nail. They even understand the concept of zero, which — as anyone who has had to teach a toddler knows — is rather difficult to grasp. No, counting is not special, but how we count is.

I don’t mean to toot our own horn, but humans are remarkable for having created numerous numeral systems, each specialized in their own ways. Ask almost anyone and they will at least have heard of binary. Hackaday readers are deeper into counting systems and most of us have used binary, octal, and hexadecimal, often in conjunction, but those are just the perfectly standard positional systems.

If you want to start getting weird, there’s balanced ternary and negabinary, and we still haven’t even left the positional systems. There’s a whole host of systems out there, each with their own strengths and weaknesses. I happen to think seximal is the best. To see why, we have to explore the different creations that arose throughout the ages. As long as we’ve had sheep, humans have been trying to count them, and the systems that resulted have been quite creative, if inefficient.

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