1. The positional encoder in Figure 1 uses Gray code to represent the position of the pointer. E.g. when the pointer is in the 3rd area, the output is 0010. Gray code is one of the codes used in digital systems. It has the advantage over binary numbers that only one bit in the code word changes when going from one number to the next; which eliminates the error when the pointer moves between areas. Example: Gray Code 0101 represents the Binary Code 0110, i.e., 6. 4 5 2 0110 0010 a. Design a combinational circuit with four inputs and four outputs that converts the four-bit gray code into an equivalent four-bit binary number. b. Use Karnaugh map technique to simplify the expression. Hint: You can rewrite the expression to use the minimum number of gates. C. Draw the circuit of the simplified form 0011 6 0111 1 0101 0001 7 00LO 0000 1000 8 15 LOLL 1001 Binary counterpart 9 LLLL LLOL 14 OLLL OLOL 10 13 11 12 Gray code Figure 1. Positional Encoder