For the math-inclined, it's easy to see why this method works. First, as tokumaru underlined, simply doing M = 2

^{N} gives the exact answer. By decomposing N into

tens and

ones, we effectively get the equivalent M = 2

^{T·10 + O}, which is M = 2

^{T·10}·2

^{O}. In this form, we can see that the tens will give you powers of 1024 (2

^{10¹} = 2

^{10} = 1024 = 1K, 2

^{10²} = 2

^{10·2} = 1024 × 1024 = 1M etc.) that is multiplied by 2

^{O}.

koitsu wrote:

OT: Then again I've always done certain kinds of math operations in a way that I would get chastised for by teachers. I have difficulty with the number numbers 7, 8, and 9 (and sometimes 6). The only exception is if they're of themselves, i.e. 7*7, 8+8, etc. I know without issue. It's when they're used with other 7-to-9 values that I have trouble. At some point I figured out on my own that I could just round up a value to an "easier" number, then subtract what I rounded up by later. Example: 17+8 for me becomes 20+8-3 thus 25. It's more work, but it's less taxing on my brain. Can't explain why, it just is. With multiplication, I vary. Example: 17*8 for me would become either (20*8)-(3*8) or (10*8)+(7*8). If I first thought of doing the 2nd method, I'd hit 7*8 and say "screw it", and instead use the 1st method, thus: 20*8=160, 3*8=24, 160-124=136.

I know this isn't efficient, even remotely, and my brain can't really handle doing anything past super basic math this way... but it's how I survived school. I need pen/paper otherwise. Here's the real kicker: if you asked me to do some basic math involving 7/8/9 without that method? I'd do what I could, then start adding additional numbers using my fingers as helpers and counting out loud. Yup, I'm 41 years old and still do this on occasion. The look on adult's faces is always the same: a smirk backed with an expression of horror, like "is he seriously counting on his fingers? Is this guy slow?" But I honestly couldn't care less -- use whatever tools you have. Kids, on the other hand, don't give me any grief.

I guess we all have the "difficult" numbers, the ones we struggle with

. I have no problem multiplying numbers, but sometimes, when the multiplicands are in the 7–9 range, my spontaneous result is wrong because I use the product from the wrong numbers (like doing 6×7 = 56, and then "oops, that's 42, 56 is 7×8"). The same thing happens with hex numbers, I tend to mentally mix up 0x0B and 0x0D, doing "0x0B = 13... oops, wrong one". And resistor color bands too, from yellow to blue ("green is 6... oops, wrong one"),

though these days, I rarely see through-hole resistors, so it's much less of an issue. And for your technique of rounding a number to the "easiest" number then subtract, I do it all the time, and I don't see it as inefficient because I'm faster with that method, probably because it allows to "guesstimate" quickly and you deal with smaller/simpler numbers. From your example 17×8, I also do (20×8)-(3×8) but even before, I think "the result is under 160", which helps me check the result mentally should I mess up numbers.