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Problem 2 Design a BCD counter that uses four(4) T flip-flops using the given table format below. The output signal Y = 0 onl

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(a.) The truth table is as follows:-

Q8 Q4 Q2 Q1 Q8 Q4 Q2 Q1 Y m TQ8 TQ4 TQ2 TQ1
0 0 0 0 0 0 0 1 1 Q8'Q4'Q2'Q1' 0 0 0 1
0 0 0 1 0 0 1 0 1 Q8'Q4'Q2'Q1 0 0 1 1
0 0 1 0 0 0 1 1 1 Q8'Q4'Q2Q1' 0 0 0 1
0 0 1 1 0 1 0 0 1 Q8'Q4'Q2Q1 0 1 1 1
0 1 0 0 0 1 0 1 1 Q8'Q4Q2'Q1' 0 0 0 1
0 1 0 1 0 1 1 0 1 Q8'Q4Q2'Q1 0 0 1 1
0 1 1 0 0 1 1 1 1 Q8'Q4Q2Q1' 0 0 0 1
0 1 1 1 1 0 0 0 1 Q8'Q4Q2Q1 1 1 1 1
1 0 0 0 1 0 0 1 1 Q8Q4'Q2'Q1' 0 0 0 1
1 0 0 1 0 0 0 0 0 Q8Q4'Q2'Q1 1 0 0 1

BCD supports only input combinations from 0 to 9, but the possible combinations of 4 variables is 16, therefore the next state for rest of the combinations (10-15) will be don't care.

(b.) The input equations for TQ4, TQ2, TQ1 are as follows:-

Q2Q1 08 Q4 OU Il 00 t 3 2. 4 5 7 6 X 12 Х 13 is 14 10 xil 8 9 X 10 Toy = Q2 Qi Q2Q1 Q8Q4 il 0 3 2 01 4 5 7 6 х 12 Х 151 Х X 8

(c.) The equation of output signal Y is as follows:-

Q2Q1 3804 3 ol ५ S 7 6 x ll 12 15 4 XX 8 lo Y = Oo + By Qi

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