# Translating binary plaintext into alphabetic plaintext using an $18$-digit base-$26$ integer system

I'm working on a cryptography problem and went through the long process of decrypting a sent message to get a $$27$$ digit number.

It then says: Plaintext blocks have $$18$$ letters and that such an alphabetic block is converted to a decimal string by considering it to be an $$18$$-digit base-$$26$$ integer (where $$A$$ represents $$0$$, $$B$$ represents $$1$$, etc.) and then taking the decimal expansion of this integer. I really have no idea of what this means or how to begin, can someone please just point me in the right direction.

For example, how would the alphabetic plaintext "HELLO" be made into a plaintext message.

In general a base-$$n$$ number has a value given by the summation of the digits multiplied by $$n^k$$ where $$k$$ is their position in the number starting at $$0$$.
For example, the number $$234=2*10^2+3*10^1+4*10^0$$ in base-$$10$$. In base $$26$$ the number represented by "HELLO" given in your example would be $$7|4|11|11|14=7*26^4+4*26^3+11*26^2+11*26^1+15*26^0=3276873$$.
• so the number I have from decrypting is $p_{1}*26^17+p_{2}*26^16+...+p_{18}*26^0$? Is that I should go about trying to solve this for an alphabetic message? – joseph Feb 24 at 20:14