I want to write the length of the word w which has the following form:
w=a^nb^mc^pd^q
with n,m,p,q >=2 after using the Run-Length-Compression. Also if w = a^2b^3c^4d^5 I can write w with the Run-Length-Compression as a0b1c00d01. The first binary number is dropped since the number 2(10),3(11),4(100),5(101) in binary representation all starts with 1 so we get
a10b11c100d101 ==> a0b1c00d01.
Now I want to write the length of the result if
w =a^nb^mc^pd^q
= a |binary(n)|-1 b |binary(m)|-1 c |binary(p)|-1 d |binary(q)|-1
= |binary(n)| |binary(m)||binary(p)||binary(q)| -4 +4
= |binary(n)| |binary(m)||binary(p)||binary(q)|
My question is there anyway to simplify the result by writing the binary(n)... as sum or something similar ?