Microsoft Word - Digital Logic Design v_4_6a

Step 2) Determine the number of flip-flop based on the number of State
(#state = 3) ≤ 2 (#flip-flop = 2) Assuming Full Coding

Step 3) Assign a Unique code to each state
a: 00, b:01; C:11

Step 4) Write the excitation-input equations:

 The T flip-flop excitation and characteristic equations are Y+ = T XOR Y and T = Y + (^) XOR Y
Note: You may derive general excitation equation from re-arranging the characteristic table
for the Tflip flop to obtain the excitation table for the T flip-flop as shown below:
 Write the PS/NS table (for T & JK, this intermediate step is helpful)

Y 1 Y 2 Y 1 + Y 2 + T 1 T 2 Z

0 0 0 1 0 1 1

0 1 1 1 1 0 1

1 1 0 0 1 1 0

1 0 - - - - 0

Unused States

T Y +^

0 Y

1 Y’

T Y Y +^

0 0 0

0 1 1

1 0 1

1 1 0

Characteristic

table

Output Excitation

table

Y Y+ T^

0 0 0

0 1 1

1 0 1

1 1 0

Input Excitation

table

T = Y + (^) XOR Y
Input Excitation Eq.

CLK

CLR’

Z (output)

Y1(msb)

a

ST = Tclk

b

ST = Tclk

c

ST = Tclk

a

ST = Tclk

b

ST = Tclk

Timing Events 1 2 3 4 5 6 7

c

ST = Tclk

1 T clk’

2 T clk’

Y2