February 2006
Intermediate to advanced
332 pages
9h 3m
English
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Hack #38. Calculate Mental Checksums
Computers use checksums to ensure that data was not corrupted in transmission. Now your brain can use a checksum for your mental math, with a few easy techniques.
It's important to have some way to check your mental math that doesn't take as long as solving the problem did originally, and ideally is much shorter. It's easy to check your math for the four basic operations of arithmetic (addition, subtraction, multiplication, and division) by calculating digit sums for the numbers involved. A digit sum is a special kind of checksum or data integrity check. Checksums are used all over the world of computing, from credit cards to ISBNs on books, to downloads you make with your web browser. Now your brain can use them, too.
Finding the digit sum of a number is easy. Just add all the digits of the number together. If the result is greater than 9, add the digits together again. Continue to do so until you have a one-digit result. If the result is 9, reduce it to 0. The result is the digit sum of the original number.1
For example, the digit sum of 381 is 3:
3 + 8 + 1 = 12 1 + 2 = 3
Similarly, the digit sum of 495 is 0:
4 + 9 + 5 = 18 1 + 8 = 9 (same as 0)
A number's digit sum is actually that number modulo 9—in other words, the remainder when that number is divided by 9. See "Calculate Any Weekday" [Hack #43] for a refresher on modulo arithmetic.
This technique is also known as casting out nines. Casting out nines and a similar technique known as casting ...
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O’Reilly covers everything we've got, with content to help us build a world-class technology community, upgrade the capabilities and competencies of our teams, and improve overall team performance as well as their engagement.Julian F.
I wanted to learn C and C++, but it didn't click for me until I picked up an O'Reilly book. When I went on the O’Reilly platform, I was astonished to find all the books there, plus live events and sandboxes so you could play around with the technology.Addison B.
I’ve been on the O’Reilly platform for more than eight years. I use a couple of learning platforms, but I'm on O'Reilly more than anybody else. When you're there, you start learning. I'm never disappointed.Amir M.
I'm always learning. So when I got on to O'Reilly, I was like a kid in a candy store. There are playlists. There are answers. There's on-demand training. It's worth its weight in gold, in terms of what it allows me to do.