Howdy. I've been struggling with a homework assignment to create a 4-bit combinational lock. I've so far created the state diagram, truth table (current state, next state etc) and karnaugh maps, but cannot simplify my equations to fit the JK format. Currently I have:

X(t+1)= I' Y' Z + I X' Z' + X Y'

Y(t+1) = X' Y Z' + I X Y' + I Y' Z + X Z

Z(t+1) = I' X' Y' + I' X' Z' + X Y' Z' + I X Y'

But of course I need it to follow the X'(Jx)+X(Kx') format. Could someone give me a hint as to how I might simplify it down? I have tried simplifying it from a POS and a SOP expression, but just can't seem to get it right. I can supply my diagrams/tables if it helps - I may have made a mistake!

EDIT: I represents the input. X, Y and Z represent the three flip-flops required, and (t+1) represents its value at the next clock cycle.

EDIT2: Just watched one of my lectures on this again, and it has totally confused me! I think I have this conversion process all wrong!

EDIT3: So by my new understanding, I've come up with this, but it means some terms are ignored:

Jx = IZ’

Kx = Y

Jy = IX + IZ

Kx = X’Z’

Jz = I’X’ + XY’

Kz = 1

I have a feeling this is wrong, but I'm just not understanding it!

X(t+1)= I' Y' Z + I X' Z' + X Y'

Y(t+1) = X' Y Z' + I X Y' + I Y' Z + X Z

Z(t+1) = I' X' Y' + I' X' Z' + X Y' Z' + I X Y'

But of course I need it to follow the X'(Jx)+X(Kx') format. Could someone give me a hint as to how I might simplify it down? I have tried simplifying it from a POS and a SOP expression, but just can't seem to get it right. I can supply my diagrams/tables if it helps - I may have made a mistake!

EDIT: I represents the input. X, Y and Z represent the three flip-flops required, and (t+1) represents its value at the next clock cycle.

EDIT2: Just watched one of my lectures on this again, and it has totally confused me! I think I have this conversion process all wrong!

EDIT3: So by my new understanding, I've come up with this, but it means some terms are ignored:

Jx = IZ’

Kx = Y

Jy = IX + IZ

Kx = X’Z’

Jz = I’X’ + XY’

Kz = 1

I have a feeling this is wrong, but I'm just not understanding it!

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