Changing to binary currency, no nickel and diming

Binary (hence computers) can not exactly reproduce 0.01 (cents) 0.05 (nickels) nor 0.10 (dimes). However binary can exactly represent 0.25 (quarters) and 0.50 (half dollars). The closest float 32 can get to 0.01 is roughly 0.009999999776482582

So maybe future currency can just get rid of pennies,nickels, and dimes, and instead just continue on the 'halfing' series:

0.5000 (half dollar) is half of 1.0 (dollar)
0.2500 (quarter) is half of 0.50 (half dollar)
0.1250 (eighth) is half of 0.25 (quarter)
0.0625 (sixteenth) is half of 0.125 (eighth)

Though writing down 0.0625 frequently can be annoying. It would be much easier to write in hex:

0.8 hex = 0.5000 dec
0.4 hex = 0.2500 dec
0.2 hex = 0.1250 dec
0.1 hex = 0.0625 dec

Though without hex alpha digits present (a-f) you wouldn't know it was hex instead of dec. Preceding with the prefix '0x' sort of defeats the goal of reducing the number of characters to write. Though perhaps hex could be the new format for currency and would be assumed after the $ dollar sign.

Hex fractions, and how to add the 4 types of 'binary coins' to create this value:

0.1 hex (01/16) (one of the 4 binary coins)
0.2 hex (02/16) (one of the 4 binary coins)
0.3 hex (03/16) = 0.1875 dec (0.2 + 0.1)
0.4 hex (04/16) (one of the 4 binary coins)
0.5 hex (05/16) = 0.3125 dec (0.4 + 0.1)
0.6 hex (06/16) = 0.3750 dec (0.4 + 0.2)
0.7 hex (07/16) = 0.4375 dec (0.4 + 0.2 + 0.1)
0.8 hex (08/16) (one of the 4 binary coins)
0.9 hex (09/16) = 0.5625 dec (0.8 + 0.1)
0.A hex (10/16) = 0.625 dec (0.8 + 0.2)
0.B hex (11/16) = 0.6875 dec (0.8 + 0.2 + 0.1)
0.C hex (12/16) = 0.7500 dec (0.8 + 0.4)
0.D hex (13/16) = 0.8125 dec (0.8 + 0.4 + 0.1)
0.E hex (14/16) = 0.8750 dec (0.8 + 0.4 + 0.2)
0.F hex (15/16) = 0.9375 dec (0.8 + 0.4 + 0.2 + 0.1)