![ANALYSIS OF CLOCKED SEQUENTIAL
CIRCUITS
State Equations
D Q
Q
CLK
D Q
Q
A
B
y
x
A(t+1) = DA
= A(t) x(t)+B(t) x(t)
= A x + B x
B(t+1) = DB
= A’(t) x(t)
= A’ x
y(t) = [A(t)+ B(t)] x’(t)
= (A + B) x’](https://image.slidesharecdn.com/lec25-26-241001175405-9978f7da/85/Digital-Logic-Design-Synchronous-logic-circuits-7-320.jpg)
Digital Logic Design Synchronous logic circuits
- 3. DIRECT INPUTS Some flip flops have asynchronous inputs that are used to force the flip flop to a particular state independent of the clock The input that sets the flip flop to 1 is called preset or direct set The input that clears the flip flop to 0 is called clear or direct reset The direct inputs are useful for bringing all flip flops in a system to a known starting state
- 4. FLIP-FLOPS WITH DIRECT INPUTS Asynchronous Reset D Q Q R Reset R’ D CLK Q(t+1) 0 x x 0
- 5. FLIP-FLOPS WITH DIRECT INPUTS Asynchronous Reset D Q Q R Reset R’ D CLK Q(t+1) 0 x x 0 1 0 ↑ 0 1 1 ↑ 1
- 6. ANALYSIS OF CLOCKED SEQUENTIAL CIRCUITS The State State = Values of all Flip-Flops Example A B = 0 0 D Q Q CLK D Q Q A B y x
- 7. ANALYSIS OF CLOCKED SEQUENTIAL CIRCUITS State Equations D Q Q CLK D Q Q A B y x A(t+1) = DA = A(t) x(t)+B(t) x(t) = A x + B x B(t+1) = DB = A’(t) x(t) = A’ x y(t) = [A(t)+ B(t)] x’(t) = (A + B) x’
- 8. ANALYSIS OF CLOCKED SEQUENTIAL CIRCUITS State Table (Transition Table) D Q Q CLK D Q Q A B y x A(t+1) = A x + B x B(t+1) = A’ x y(t) = (A + B) x’ Present State Input Next State Output A B x A B y 0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 1 1 0 1 1 1 t+1 t t 0 0 0 0 1 0 0 0 1 1 1 0 0 0 1 1 0 0 0 0 1 1 0 0
- 9. ANALYSIS OF CLOCKED SEQUENTIAL CIRCUITS State Table (Transition Table) D Q Q CLK D Q Q A B y x A(t+1) = A x + B x B(t+1) = A’ x y(t) = (A + B) x’ Present State Next State Output x = 0 x = 1 x = 0 x = 1 A B A B A B y y 0 0 0 0 0 1 0 0 0 1 0 0 1 1 1 0 1 0 0 0 1 0 1 0 1 1 0 0 1 0 1 0 t+1 t t
- 10. ANALYSIS OF CLOCKED SEQUENTIAL CIRCUITS State Diagram Present State Next State Output x = 0 x = 1 x = 0 x = 1 A B A B A B y y 0 0 0 0 0 1 0 0 0 1 0 0 1 1 1 0 1 0 0 0 1 0 1 0 1 1 0 0 1 0 1 0 D Q Q CLK D Q Q A B y x 0 0 1 0 0 1 1 1 0/0 0/1 1/0 1/0 1/0 1/0 0/1 0/1 AB input/output
- 11. ANALYSIS OF CLOCKED SEQUENTIAL CIRCUITS D Flip-Flops Example: D Q Q x CLK y A Present State Input Next State A x y A 0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 1 1 0 1 1 1 0 1 1 0 1 0 0 1 0 1 00,11 00,11 01,10 01,10 A(t+1) = DA = A x y