Design a system which consists of three components, a counter, a display driver, and a seven-segment as shown below.

a. Design the counter using four JK flip flops A, B, C and D and a minimum number of gates. The counter is binary coded decimal , using 2421 code as shown in Table 1 below and is to go through the sequence:

0 3 6 9 2 5 8 1 4 7 and repeat

Thus, the counter sequences 0000, 0011, 1100, 1111, 0010, etc. After completing the design of this counter, draw a state diagram.

Table : Binary Coded Decimal codes

Decimal Digit 2421 Code
0 0000
1 0001
2 0010
3 0011
4 0100
5 1011
6 1100
7 1101
8 1110
9 1111
unused 0101
0110
0111
1000
1001
1010

b. The outputs of the counter are inputs to the display driver. It is just a four-input, seven-output combinational circuit. If one of the unused codes turns up (for example, the counter is turned on and ABCD =0111), the display should be blank (that is, all seven inputs should be 0). Find the equations for the implementation of the X1, X2, X2, X4, X5, X6 and X7 on the seven segment
c. Implement the seven segment circuit using a ROM similar to the one below:
a. Draw the ROM truth table for the seven segment
b.Implement the combinational circuit for the seven segment using a ROM