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’