7.a. How did computer architects determine how many bits were needed?

They knew they needed to represent:

Upper case characters: 26

Lower case characters: 26

Digits: 10

Special Characters:

(! + ( ) . ? / * - % & # =, etc.) 32 (?)

---------

94

So they needed:

log(I)/log(2) = log(94)/log(2) = 1.973/0.301 = ceiling of (6.55)

= 7 bits

which we know since 2⁶ = 64 (not enough) and 2⁷ = 128 (more than enough)