1. (15 points) Write a POS expression for a 2-to-1 MUX (multiplexer) 2. (80 points) Consider a function F with 4 bits of input A3,A2,A1,Ao such that the output of F is 1 if the unsigned binary number represented by A3A2AAo is a prime (i.e., 2, 3, 5,7, 11 or 13) Otherwise, the output of F is 0 a) (15 points) Write the truth table for F b) (15 points) Based on the truth table, implement F using a 16-to-1 MUX and nothing else c) (15 points) Based on the truth table, implement F using a 8-to-1 MUX, some AND gates, some OR gates, and some NOT gates. d) (15 points) Based on the truth table, implement F using a 4-to-1 MUX, some AND gates, some OR gates, and some NOT gates. e) (20 points) Using Shannon's expansion, implement F using a 2-to-1 MUX, some AND gates, some OR gates, and some NOT gates. 3. (65 points) A 4-bit rotator circuit is defined in the last two slides in the mini-lecture notes of Class 21. This rotator rotates the input bits to the left by 0, 1, 2 or 3 bit positions. We call it a left-rotator. A right-rotator is the same as a left-rotator except that it rotates to the right instead of to the left. In this question, you are asked to design a right-rotator circuit using one left-rotator a) (30 points) Design a right-rotator by converting its X Y inputs by some AND, OR, and NOT gates into the X Y inputs to the left-rotator such that the left-rotator will behave like a right- rotator. Note that you are not allowed to modify the internal circuitry of the left-rotator b) (35 points) Design a right-rotator with one left-rotator and without any other gate. Note that you are not allowed to modify the internal circuitry of the left-rotator