Currency that Fits

Note: This Idea is being presented in detail from the perspective of the US, but there is no reason why the arithmetic presented herein (in the solution to existing US-centric problems) cannot work for any national currency.

Also note: I think this idea was posted here a while back, but it was only as an annotation to someone else's idea, and I cannot find it, so I suppose it (annotation or whole idea) has been deleted (I suspect the latter). So, because I think my annotation was unique enough to stand on its own, here goes:

One of the problems with the US currency system is that there are too many denomination types to fit in cash register drawers. At various times there have been $1, $2, $5, $10, $20, $50, and $100 bills in wide use, but most cash register drawers only have 5 slots (one usually reserved for personal checks). As a result, $2 bills have generally been rejected from circulation, and $50 and $100 bills usually get hidden UNDER the cash drawer, to reduce incentive for theft. OK.

But there is another problem. The US Mint printed $2 bills for a reason, and that was simply to reduce the total number of $1 bills in circulation (they have an average lifespan of less than a year, so the Mint is ALWAYS printing lots of them, just to replace the worn-out ones -- expensive, see?). If only the $2 bill was not rejected, then fewer total bills would be in circulation, yet the total number of $ in circulation would be the same (and printing costs would go down, saving tax dollars). But where to put them in the cash register drawer?

AND there is another problem: Inflation is causing production of $100 bills to be ramped up, and the Treasury Department really does NOT want to put $500 bills into wide circulation (it forces drug dealers to carry around larger volumes of cash, which makes them more easily notice-able, and capture-able). But inflation is going to cause average folks to want to have something more convenient than a wad of $100 bills (on those occasions when such is warranted).

Do note that the $20 bill exists for the same reason that the $2 was created: When the next-higher denomination is broken into change, would need four $10 bills or four $1 bills. Having the intermediate denomination means counting change can be faster, involving fewer bills (and requiring fewer in overall circulation). Also note that there is no $200 bill, which might be a numerically-consistent answer to the inflation problem.

Well folks, there is an alternate and pretty simple solution to all those problems. It will involve getting people to exercise their arithmetic skills a little more (but counting money is how most people learn simple arithmetic in the first place, heh), and I'm sure that all who hate math will now fishbone this idea and read no further. So be it.

Let the Mint STOP making $5, $10, $20, $50, and $100 bills altogether, and replace them with $4, $16, $64, and $256 bills. This works much more smoothly than you might expect, when making change from a larger denomination:
Break a $4 bill into three $1 bills, plus coins.
Break a $16 bill into three $4 and three $1 bills, plus coins.
Break a $64 bill into three $16, three $4, and three $1 bills, plus coins.
Break a $256 bill into three $64, three $16, three $4, and three $1 bills, plus coins.
(Of course, if one does not want to break a larger denomination all the way down to receive $1 in coins, then alter any single word "three" above to become "four", and stop the sequence.)

In the cash register drawer would easily fit $1, $4, $16, and $64 bills, with that fifth slot still reserved for personal checks. Remember that the same inflation which will encourage the use of bills larger than $100 will also make both $50 and $64 amounts less desire-able for theft, so eventually having them in the cash drawer will become reasonable. Meanwhile, of course, the larger $256 bills would still go "securely" under the drawer. (The Mint could let $500 bills go extinct, knowing that the next "natural" denomination in this system would be for $1024 -- and actually printing such a bill may not be necessary. A $1000 under this system would be broken down into three $256, three $64, TWO $16, and two $4 bills (without bothering with $1 bills or any coins.) --and of course the Mint would want to keep $1000 bills out of circulation, anyway.)

Next, the Mint benefits by not needing to print so many $1 bills, because fewer are needed to make change from $4 bills than from $5 bills. $2 bills can be welcomed into extinction -- and the equivalent problem involving $10, $20 and $50 bills disappears because of that intermediary $16 denomination.

Finally, when someone answers a $64 Question, payment will be easy!