Open Book / Open Notes

EGRE 254 Quiz #2 Open book / Open notes 4/13/09

Name: _SOLUTIONS_ Neatly print your name.

1 1. a). Using the minimum amount of additional combinational logic, show how to implement a JK flip-flop using a T flip-flop. You do not need to draw the circuit. Just write the equation for T.

J Q 0 0   Q 1   1 K T(d Q )= ( D ,� ; d ) + JQ KQ dQ J K Q T Q C /Q CLK Q TFF

b). Using the minimum amount of additional combinational logic, show how to implement a JK flip-flop using a D flip-flop. You do not need to draw the circuit. Just write the equation for D. D(d Q )= ( D ,1; d ) = JQ + KQ dQ J K Q D Q C /Q CLK Q TFF

2 2. Fill in the Q maps and the Z map for the given state diagram.

X = 0 X = 0

X = 1 X = 1 S0 S1 S2 Q Q Q Q X = 0 Q Q 1 2 1 2 1 2 0 0 0 1 1 0 Z = 0 Z = 1 Z = 1

X = 1 X = 0 X = 1 S3 Q Q 1 2 1 1 Z = 0 Q1 Q1 Q1 Q2 Q1 Z 0    0   0 0 1

X 0  1 1 X   1  Q2 1 0

3 3. Fill in the state table for the state diagram shown below.

X = 0 X = 0

X = 1 X = 1 S0 S1 S2 X = 0 Z = 0 Z = 1 Z = 1

X = 1 X = 0 X = 1 S3

Present Next state State X=0 X=1 Z S0 S0 S1 0 S1 S2 S2 1 S2 S0 S3 1 S3 S0 S3 0

4 4. Given the Q maps, write the simplest sum of product equations for designing the finite state machine using SR flip-flops. S(Q) = (; d, 1), R(Q) = (; d, 0)

Q1 Q1 Q1 Q2 0 0 1 1 0 1 1 0 0 ∆ 1 1 ∆ 1 1 ∆ Y Y d d d d d d d d X X 0 0 1  0   0

YQ S1 = 2 S2 = Y corrected

R1 = XQ2 R2 = X

5. Given the Q maps, write the simplest sum of product equations for designing the finite state machine using D flip-flops. D(Q) = (, 1; d)

D1 = XQ1+ YQ 2 + Q 1 Q 2 D2 = XQ2 + Y Corrected

5 6. Given the Q maps, write the simplest sum of product equations for designing the finite state machine using T flip-flops. T(Q) = (, ; d)

T1 = YQ1 Q 2+ XQ 1 Q 2 T2 = XQ2+ YQ 2

6 7.. Given the Q maps, write the simplest sum of product equations for designing the finite state machine using JK flip-flops. J(Q) = (; d, 1, ), K(Q) = (; d, 0, )

J1 = YQ2 J2 = Y

K1 = XQ2 K2 = X

8. Assuming the machine in problem 7 has been built using JK flip-flops. Fill in the Q* maps. Be sure to enter either 0 or 1 in the cells that were don’t care conditions. * * Q1 Q1 Q1 Q2 0 0 1 1 0 1 1 0 0 1 1 1 1 1 1 1 Y Y 0 1 1 0 1 0 0 1 X X 0 0 1 0 0 0 0 0

The characteristic equation for the JK flip-flop is Q* = JQ + KQ ; therefore,

* Q1= J 1 Q 1 + K 1 Q 1 = YQ 2 Q 1 + X Q 2 Q 1 = YQ 2 Q 1 + XQ 1 + Q 1 Q 2 * Q2= J 2 Q 2 + K 2 Q 2 = YQ 2 + XQ 2