Question

C- For the following circuit, find the state and the outputs of the flip flops for three clocks. Assume that all flip flops are initially (A = 1, B = 1) and the input x = 0. Clock statc J-K flip flop J-K flip flop state A|A | state BB Initial state Clock Clock Clock

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Answer 1

Let we consider the input of first flip flop J1, K1 and second J2, K2 and draw the diagram

From the above diagram the equation of the J-K flip flop:

хи z =7 at XB Вх to la , CD, 3X к, а Ã X Clock

J1 = {B, K1 = x

And for second flip flop:

J2 = 7, K2 = ĀX

The equation for output Z:

z = Āx + Bx

In the First clock:

Assume that the initial conditions are:

A = 1, B = 1 and x = 0

The input of the first flip flop:

J1 = {B, K1 = x

J1 = 1.1, K1 = 0

J1 =1, K1 = 0

From the truth table of J-K flip flop,

Inputs J K CLK 0 0 0 1 10 11 Outputs Q Comments 9No change 0 1 Reset 10 Set ©. Q. Toggle

the output of the first flip flop is:

A = 1,Ā = 0

Assume that the initial conditions are:

A = 1, B = 1 and x = 0

The input of the second flip flop:

J2 = 7, K2 = ĀX

J2 = 7, K2 = 1.0

J2 = 1, K2 = 0

From the truth table of J-K flip flop, the output of the second flip flop is:

B = 1, B = 0

The output Z:

z = Āx + Bx

z = 10 + 1.0

z = 0

Now the output of flip flop after the first clock:

A = 1, B = 1

The output Z:

z = 0

In the second clock:

A = 1, B = 1, x = 0

The input of the first flip flop:

J1 = {B, K1 = x

J1 = 1.1, K1 = 0

J1 =1, K1 = 0

From the truth table of J-K flip flop, the output of the first flip flop is:

A = 1,Ā = 0

The input of the second flip flop:

J2 = 7, K2 = ĀX

J2 = 7, K2 = 1.0

J2 = 1, K2 = 0

From the truth table of J-K flip flop, the output of the second flip flop is:

B = 1, B = 0

The output Z:

z = Āx + Bx

z = 10 + 1.0

z = 0

Now the output of flip flop after the second clock:

A = 1, B = 1

The output Z:

z = 0

In the Third clock:

A = 1, B = 1, x = 0

The input of the first flip flop:

J1 = {B, K1 = x

J1 = 1.1, K1 = 0

J1 =1, K1 = 0

From the truth table of J-K flip flop, the output of the first flip flop is:

A = 1,Ā = 0

The input of the second flip flop:

J2 = 7, K2 = ĀX

J2 = 7, K2 = 1.0

J2 = 1, K2 = 0

From the truth table of J-K flip flop, the output of the second flip flop is:

B = 1, B = 0

The output Z:

z = Āx + Bx

z = 10 + 1.0

z = 0

Now the output of flip flop after the third clock:

A = 1, B = 1

The output Z:

z = 0

State J-K Flip flop statel T-K Flip Flop - State A A State state 8/3 B 13 Initial L state clona 210 | 101101110 IClock Clock ili olo, olio