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Finding the fun in good math; Shredding bad math and squashing the crackpots who espouse it.
Mark Chu-Carroll (aka MarkCC) is a PhD Computer Scientist, who works for Google as a Software Engineer. My professional interests center on programming languages and tools, and how to improve the languages and tools that are used for building complex software systems.
Category: manual computing devices
To do multiplication with your fingers in binary is very easy: it's just a mixture of addition and bit-shifting. The only real trick is memory: to multiply a×b, you need to remember the binary digits of both x and y,...
Posted by Mark C. Chu-Carroll at 10:14 PM • 14 Comments •
Category: manual computing devices
There is another way of doing math on your fingers, which gives you a much greater range of numbers, and which makes multiplication particularly easy. It's a bit more work to get used to than the finger abacus, but it...
Posted by Mark C. Chu-Carroll at 4:12 PM • 11 Comments •
Category: manual computing devices
Suppose you want to do some math, but you don't have an abacus handy. Oh, the horror! What do you do? No problem! Your hands make a great two-digit soroban-type abacus. The four beads on the lower deck are your...
Posted by Mark C. Chu-Carroll at 8:57 PM • 15 Comments •
Category: manual computing devices
Doing square root on the abacus is a lot like doing it on paper. The big difference? It's actually easier on the abacus. What I find pretty cool is that I'm a rank beginner at the abacus. I never actually...
Posted by Mark C. Chu-Carroll at 9:47 PM • 9 Comments •
Category: manual computing devices
To do a square root on an abacus, you use partitions to do a paper algorithm for square root using the abacus. The catch is that most people don't even remember how to do square roots on paper, if they...
Posted by Mark C. Chu-Carroll at 11:07 AM • 22 Comments •
Category: manual computing devices
Now we're going to try something challenging on the abacus: division. Like multiplication, abacus division is close to the way you'd do it on paper. But just like doing paper division is trickier than paper multiplication, abacus division is tricker...
Posted by Mark C. Chu-Carroll at 11:02 AM • 5 Comments •
Category: manual computing devices
Once you can add on an abacus, the next thing to learn is multiplication. Like addition, it follows pretty closely on the old pencil-and-paper method. But it's worth taking the time to look closely and see it step by step,...
Posted by Mark C. Chu-Carroll at 7:33 PM • 5 Comments •
Category: manual computing devices
If you want to talk about mechanical computing tools, you can't ignore the abacus. It's the oldest computing tool in the world; and it's still very commonly used. It's also about as different from the slide rule as you could...
Posted by Mark C. Chu-Carroll at 3:45 PM • 17 Comments •
Category: manual computing devices
Slides rules are actually astonishingly powerful things. The simple slide rule does multiplication and division using the C and D scales; strictly speaking, you can have a basic rule with nothing but C and D. But you almost never see...
Posted by Mark C. Chu-Carroll at 9:04 PM • 5 Comments •
Category: manual computing devices
Several people in the geekout thread asked me to explain how a sliderule works, and I've been meaning to write a couple of article about manual computing devices. So I thought I'd do it. There's a nice slide-rule simulator at...
Posted by Mark C. Chu-Carroll at 6:30 PM • 25 Comments •
