Determine which of the machines with the following specifications is realizable with a finite number of states.
1) A machine is to produce an output of 1 whenever the number of 1's in the input sequence exceeds the number of 0's. For example, if the input is 01100111, the required output is 001000011;
2) A machine is to produce an output of 1 whenever the product of the number of 1's in the input sequence and the number of 0's in the input sequence is equal to 10 100 .
3) A machine that produces an output of 1 whenever the input has been one for eight or more consecutive clock cycles.