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Computers can't count
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November 5, 1998 by Gil Bates |
From...
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(IDG) -- What amazes me most is not that the year-2000 (or Y2K) problem exists, it's that people are surprised about it. If you look back at even half of the life span of InfoWorld, you'll find no shortage of cases that prove computers have real difficulties with numbers.
Who can forget the notorious "Pentium flaw" scandal of 1994? The P60 problem, as I like to call it, was less widespread than Y2K (unless you happened to have a new Pentium system, that is) and less potentially cataclysmic (unless you were Andy Grove, and had to eat crow). So a few thousand chips didn't turn up accurate results past the sixth decimal point because of a faulty floating-point unit -- serious stuff if you're doing rocket science, not so very serious if you're doing a departmental budget. But, however you slice it, it's significant proof that computers aren't entirely reliable when it comes to figgerin'.
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More widespread, and more embarrassing to those responsible, was the great Windows Calculator scandal -- the W3.x problem. This also came to light in 1994, but it had been an issue since Windows 3.0 appeared in 1990. CALC.EXE couldn't handle simple arithmetic. I mean, really simple, obvious computations. How obvious? You do the math ...
0-2.11=-2.11, right? Microsoft's Windows 3.x Calculator agrees. Now try this: -2.11+2.1. Obviously -0.01. But between 1990 and 1994, Microsoft disagreed: The Windows 3.x Calculator said -0.00 (an interesting numeric concept, but not the right answer).
You may consider this to be bad math, but it's math like this that made a certain industry maven by far the richest man in the world. Go figure. Just don't go figure with the Windows 3.x Calculator.
Maybe it's expecting a little too much for early versions of Windows to handle math well. After all, there's ample evidence that Windows can't even count in evenly spaced denominations.
Consider the version numbering of the thing. It leaped from the simple single-digit versions, such as 1, headlong into triple figures with the late 1987 release of Windows/386 -- six months after Microsoft announced it would ship Version 2.0.
Less than three years later, Windows careened back to Version 3.0 without so much as graceful long division. With the gradual release of Version 3.1 and Version 3.11, Windows lulled its owners into a false sense of linear progression, then leaped headlong into Version 95, and from thence to OSR1, OSR2, and finally Version 98. Not even slouching middle-school teenagers who can't keep their boxer shorts below their belt line have this much trouble counting.
But there's a much larger and more prevalent problem with computer numeration. And it gets larger as you deal with larger numbers. Here's the deal: No computer has a handle on the number 1,000. They're all off by at least 2.4 percent.
Don't believe me? Well, answer this series of questions and dispel that doubt: How many meters in a kilometer? That would be 1,000. How many grams in a kilogram? Why, 1,000, natch. And how many bytes in a kilobyte? Err ... 1,024.
There it is. A whole additional 24 bytes. And the problem compounds given the larger the units you deal with. Get this: There are 1,024 kilobytes in a megabyte. That's 1,048,576 bytes ... a whopping 48,576 greater than the number you'd expect to see.
It goes without saying that this mathematical relationship does not hold true with kilometers and megameters. Nor are there more than 1 billion grams in a gigagram.
Now this is all bad enough, but computer scientists have known about the "#1K" problem for years and have shrugged it off as binary -- 2 raised to the power of 10 makes 1,024, they say.
I'd have fallen for this excuse, except that the math didn't work out. I tried it twice on Windows 3.1's Calculator on my four-year-old Pentium and got a completely different result.
Because of all this, I'm pretty confident that we'll all get past the year 2000 without a glitch. The year 2048 -- now that's another story.
Gil Bates is a free-lance Web-site columnist currently working on his first book, The Complete Idiot's Guide to Dummies. He can be reached at gilbates@technologist.com.