5.2.a. Design a 4 bit counter that counts from 0 to 15 (modulo 16) by writing the equation for input of each of 4 D-flip flops. That is the inputs to the 4 D-FFs are D[3], D[2],DI1, and D[O]. Assume the counter's outputs are C13], C12], C[1], CIO [Hint, each FF can be made to toggle by using a 2 input XOR gate as its input with one input tied to the FF output and one input based on some expression : eg. D[31-C[3] ^ ( some expression ) j. 5.2.b Design a counter that counts down from 15 to 0 (modulo 16) by writing the equation for each input of each of 4 D-flip flops. That is the inputs to the 4 D-FFs are DI3], D[2], DI1], and DIO]. Assume the counter's output is C[3], C[2], C[1], CIO]. 5.2.c. Given a counter that counts up which you can't change, how can you generate a sequence that counts down by modifying the output the counter with logic. (Hint: It might be helpful to write the sequence binary digits that count up and next to that the sequence of binary digits that counts down and see if there is a simple transformation between the two That is, find a transformation from C[3:0] that counts up to Y[3:0] that counts down. Express your answer 4 expressions for Y[3], Y[2], Y[1] and Y[0] in terms of C[3:0]. C13] C12] CI1 Y121 Up counter Y[0) clk 5.2.a. Design a 4 bit counter that counts from 0 to 15 (modulo 16) by writing the equation for input of each of 4 D-flip flops. That is the inputs to the 4 D-FFs are D[3], D[2],DI1, and D[O]. Assume the counter's outputs are C13], C12], C[1], CIO [Hint, each FF can be made to toggle by using a 2 input XOR gate as its input with one input tied to the FF output and one input based on some expression : eg. D[31-C[3] ^ ( some expression ) j. 5.2.b Design a counter that counts down from 15 to 0 (modulo 16) by writing the equation for each input of each of 4 D-flip flops. That is the inputs to the 4 D-FFs are DI3], D[2], DI1], and DIO]. Assume the counter's output is C[3], C[2], C[1], CIO]. 5.2.c. Given a counter that counts up which you can't change, how can you generate a sequence that counts down by modifying the output the counter with logic. (Hint: It might be helpful to write the sequence binary digits that count up and next to that the sequence of binary digits that counts down and see if there is a simple transformation between the two That is, find a transformation from C[3:0] that counts up to Y[3:0] that counts down. Express your answer 4 expressions for Y[3], Y[2], Y[1] and Y[0] in terms of C[3:0]. C13] C12] CI1 Y121 Up counter Y[0) clk