(1) [15pts](a) Convert the BCD coded number below to equivalent decimal form:
(c) Design a circuit for converting a 4-bit Gray code into its binary equivalent. You may use AND, OR, XOR, or inverter gates only. Use as few gates as possible.
(d) Implement a 1-bit full adder using a minimum number of 4-input, two control-line multiplexers and inverters only. An inverter counts as 1/5th (20%) of a MUX. Assume complements are not available.
(3) [20pts] A JN flip-flop has two inputs, J and N. Input J behaves like the J input of a JK flip-flop, and N behaves like the complement of the K input of a JK flip flop (i.e. ).
(ii) Show that by connecting the two J and N inputs together, one obtains a D-type flip-flop.
(b) Derive a State Transition Table from your graph, also in Moore form.
(c) If the idle state is encoded as Y1 Y2 = 0 0, State A is encoded as Y1 Y2 = 0 1 and State B as Y1 Y2 = 1 1, derive the Karnaugh maps for the next-state and output functions.
(d) If the machine is to be implemented using JK flip-flops, obtain the Karnaugh maps for the JK flip-flop excitation inputs. Write the excitation input and external output equations for the design.