You are given a single byte A of 8 bits You have to now nd a

You are given a single byte A (of 8 bits). You have to now nd all possible ways in which the parity ofthe bits can be odd – i.e., there must be one bit set, three bits set, ve bits set, or seven bits set.
In how many different ways can this be done?

Solution

FOR 1 BIT YOU HAVE 8 DIFFERENT WAYS

FOR 3 BITS YOU HAVE 6 DIFFERENT WAYS

FOR 5 BITS YOU HAVE 4 DIFFERENT WAYS

FOR 7 BITS YOU HAVE 2 DIFFERENT WAYS

SO YOU HAVE 8+6+4+2 = 20 DIFFERENT WAYS TO DO THIS