Microsoft Word - Digital Logic Design v_4_6a

Step 2) Determine the number of flip-flop based on the number of states.
For full encoding (#states = 4) ≤ 2 (#flip-flop = 2).

Step 3) Assign Unique code to each state.
Already done in the state diagram.

Step 4) Write the excitation-input equations
The D flip-flop excitation equation is D = Y +.^
All we need is the K-map for each of the desired outputs Y 1 + ,Y 2 +, RCO:

0 0 1 0^

1

0

1

00

01

11

10

Y1Y2

D1 = Y1+

D1 = Y1’.Y2 + Y1.Y2’

D1 = Y1 XOR Y2

1

0

0

1

00

01

11

10

Y1Y2

D2 = Y2+

D2 = Y2’

0

0

1

0

00

01

11

10

Y1Y2

RCO

D2 = Y1.Y2

Excitation-inputs and output RCO equations

derived from separate K maps

(These equations are also called design equations)

00

01

11

10

1 0 0

0 0 1

1 1 0

A composite K-map is a short

hand for multiple K-maps.

Y1Y2 Y1 + Y2+ RCO

Asynchronous Present Next Present

Clear Input State State Output

CLR’ Y1 Y2 Y1 + Y2+ RCO

1 0 0 0 1 0

1 0 1 1 0 0

1 1 0 1 1 0

1 1 1 0 0 1

0 X X 0 0 0

Present State / Next State (PS/NS) Table

Present Next Present

State State Output

Y1 Y2 Y1+ Y2 + RCO

0 0 0 1 0

0 1 1 0 0

1 0 1 1 0

1 1 0 0 1

Simplified PS/NS Table

(Note: CLR’=0  Y1Y2=00)