101 Bit Dance Font 101

A hex- and bit-friendly OpenType font. Try it out by typing some numbers below!

Download the font: liberation_binary.otf
Why... any of this? the best way to count

I have 12 apples. If I give you 7, I'll have B remaining. (B is just the hex shorthand for 1011, which is 2 more than 9 in hex)

Cab is my favorite word, and CAB is my favorite number.

101010101010
x             3    
>   101010101010
+  101010101010
=  1,1111,1111,1110 (QED :)

Big number better with "shift":
1.11<<F = 1110,0000,0000,0000
        
Count by 3's:
3,6,9,C,F,12,15

a number is divisible by 3 if the difference of the count of its even 1's and the count of its odd 1's is divisible by 3. The secret key to remember is .555... = 1/3.

You can use "R" for repeating digits: So 1/11 = R01

Count by 5's:
5,A,F,14,19,1e

a number is divisible by 5 if the even and odd base 4 groupings have a difference divisible by 5. The secret key to remember is .333... = 1/5

Lets find 1/B using long division:

0.0001011101
1011\1.0 0 0 0 0 0
-      1011  0 0 0
         101  0 0 0
-        1011  0 0
          1001  0 0
-         1011 0 0
           0111 0 0
-          1011  0
            0011  0
-            1011 
                 1
                 
(Yeah, long division is gross even in binary. But at least the "guess and check" step is gone)

An easier way to find 1/n for any n is to find n's "magic sequence": Start with 1, multiply by 2 modulo n, and repeat until you arrive back at 1. So for 1/B:
1,2,4,8,5,A,9,7,3,6,1
Then put a 1 wherever the number decreased, and a 0 elsewhere:
0.0   0    0     1    0     1     1    1   0   1  = 0.00010,11101 (Note the complementary symmetry present in cyclic expansions)

For 1/E:
1,2,4,8,2,4,8,
0. 0    0    0      1     0     0     1 ... = 0.0,001,001, which of course is just half of 1/7