I am an Electrical Engineering student but my question is related to number systems, more specificaly to conversions between octal, hexadecimal and binary systems. I know the rules of conversions but I don't get one thing: why is it possible to convert hexadecimal or octal to binary by just substituting sequences of 3 or 4 digits to corresponding digit in the given system? I know that with a string of length three you can uniquely represent one member of a set with eight members. But after this kind of substitution this two representations must also have one important additional property: the sum of individual digits multiplied with the radix to the power of the digits weigth must be equal for both representations.
p.s. I apologize in advance for not using mathematical formulas as I don't know how :) Thanks.