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Synchronous non-sequential binary counter

  • Thread starter tuzza
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I am required to design a synchronous binary counter using jk flip-flops giving the count sequence: 0, 8,9,4,7,2,1,0

I have derived the excitation table using 4 jk flip-flops, however when using karnaugh maps to minimise or trying to use the unminimised function in a circuit I am unable to get it working.

Here is my excitation table:
Code:
Present state	Next state	                          Flip-flop inputs
Q3	Q2	Q1	Q0	Q3	Q2	Q1	Q0	J3	K3	J2	K2	J1	K1	J0	K0
0	0	0	0	1	0	0	0	1 	X	0	X	0	X	0	X
1	0	0	0	1	0	0	1	X	0	0	X	0	X	1	X
1	0	0	1	0	1	0	0	X	1	1	X	0	X	X	1
0	1	0	0	0	1	1	1	0	X	X	0	1	X	1	X
0	1	1	1	0	0	1	0	0	X	X	1	X	0	X	1
0	0	1	0	0	0	1	0	0	X	0	X	X	0	0	X
0	0	0	1	0	0	0	0	0	X	0	X	0	X	X	1
from this I have obtained the unminimised functions for each flip flop:
( ' denotes not )

J3 = 'q3.'q2.'q1.'q0
K3 = q3.'q2.'q1.q0

J2 = q3.'q2.'q1.q0
K2 = 'q3.q2.q1.q0

J1 = 'q3.q2.'q1.'q0
K1 = don't care

J0 = q3.'q2.'q1.'q0 + 'q3.q2.'q1.'q0
K0 = q3.'q2.'q1.q0 + 'q3.q2.q1.q0 + 'q3.'q2.'q1.q0

Can anyone tell me what I am doing wrong? Any help would be much appreciated.

Thanks
 

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