1. Develop the implementation-level state and output tables for a state machine that will read in a sequence of binary digits, one at a time, and will light a lamp if the decimal value represented by the sequence is divisible by 3. Assume reading is to start with the leftmost digit. implement the machine using appropriate 2-to-1 or 4-to-1 or 8-to-1 multiplexers.2. Design a circuit using one 16-to-1 multiplexer with four inputs X, Y, Z, and W and one output. The output should be a one whenever the four bit combination corresponds to a digit in your student ID number or 15-a digit in your student ID number. Give the truth table and then show inputs to the multiplexer.