CDA 3200 Digital Systems. Instructor: Dr. Janusz Zalewski Developed by: Dr. Dahai Guo Spring 2012
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1 CDA 3200 Digital Systems Instructor: Dr. Janusz Zalewski Developed by: Dr. Dahai Guo Spring 2012
2 Outline SR Latch D Latch Edge-Triggered D Flip-Flop (FF) S-R Flip-Flop (FF) J-K Flip-Flop (FF) T Flip-Flop (FF) Flip-Flops (FFs) with Additional Inputs
3 SR Latch (1/17) Combinational circuits Outputs depend on present inputs Sequential circuits Outputs depend on both present and the past sequence of inputs. Have memory.
4 SR Latch (2/17) Input Combinational Circuit Output Input Set 1 Output Set 1 Input Set 2 Sequential Circuit Output Set 2
5 SR Latch (3/17) X Y NOR The circuit can assume an initial and stable state: SR/PQ=00/10.
6 SR Latch (4/17) X Y NOR SR/PQ=10/01 is also stable.
7 SR Latch (5/17) X Y NOR SR/PQ=00/01 is also stable.
8 SR Latch (6/17) X Y NOR SR/PQ=01/10 is also stable. SR/PQ=00/10 is also stable.
9 SR Latch (7/17) X Y NOR
10 SR Latch (8/17) X Y NOR
11 SR Latch (9/17) PQ=01 SR=00 PQ=10 PQ=01 PQ=01 PQ=10 SR=10 SR=01 PQ=10 The change between any two of 00, 10, 01 will reach a stable state.
12 SR Latch (10/17) X Y NOR What is PQ when the circuit is stable?
13 SR Latch (11/17) SR=11 is restricted in SR latch. PQ cannot be both 1.
14 SR Latch (12/17) When SR=10, PQ=01 is stable. When SR=01, PQ=10 is stable. When SR=00, both PQ=10 and PQ=01 are stable. Note In the stable states, P=Q Any change to SR=00 will not change PQ. SR=00 is used to keep states (remember what happened.)
15 S: Set Q R: Reset Q SR Latch (13/17)
16 SR Latch (14/17) How to draw a truth table for an SR latch? Input? Output?
17 S R Q Q X X SR Latch (15/17)
18 SR Latch (16/17) Alternatively, an SR latch can be realized using NAND gates.
19 SR Latch (17/17) Alternatively, an SR latch can be realized using NAND gates. S-bar R-bar Q Q X X
20 Gated D Latch (1/3) Q + What are S and R when G=0? G=0 keeps states: Q + =D. Can SR=11 ever occur? Q + =D when G=1.
21 Gated D Latch (2/3) No do not care terms.
22 Gated D Latch (3/3) if(g==1){ Q + = D; }else{ Q + = Q; }
23 Edge-Triggered D Flip-Flop (FF) (1/3) If the G signal in the D latch is connected to a clock input, the output changes only in response to the clock, not to a change in D. And we call this latch a D Flip-Flop (FF). Q + =D
24 Edge-Triggered D Flip-Flop (FF) (2/3)
25 Edge-Triggered D Flip-Flop (FF) (3/3) Note Q does not change during Ck=0. Timing for D Flip-Flops (FF) (Falling-Edge Trigger)
26 S-R Flip-Flop (FF) (1/3) Q + changes in response to the clock signal.
27 S-R Flip-Flop (FF) (2/3) CLK When CLK=0 P + =S 1 +R 1 P When CLK=1 Q + =P
28 S-R Flip-Flop (FF) (3/3) Why master-slave Flip-Flops (FFs)? The master Flip-Flop (FF) holds the output for in the first half clock cycle. When the slave Flip-Flop (FF) updates and outputs, the master is closed. This mechanism guarantees that the final output changes only once in a clock cycle.
29 JK Flip-Flop (FF) (1/2) An extended version of the SR Flip-Flop (FF) J corresponds to S K corresponds to R J K Q Q JK can be 11. This configuration changes the state of Q.
30 JK Flip-Flop (FF) (2/2) S1=J * Q * CLK R1=K * Q * CLK S1 and R1 cannot be 1 at the same time.
31 T Flip-Flop (FF) (1/2) T=0 no state change T=1 state changes TQ Q Q + =T xor Q
32 T Flip-Flop (FF) (2/2)
33 Summary (1/8) All the Flip-Flops (FFs) and D latch are based on SR latch. SRlatch can be described using Q + =S+R Q S=1 sets Q R=1 resets Q SR=00 keeps states (Q does not change.)
34 Summary (2/8) Q + =S+R Q Gated D latch S=DG R=D G When G=0, SR==00 state kept. When G=1, Q=D When D=0, SR=01 reset Q Q=0 When D=1, SR=10 set Q Q=1
35 Summary (3/8) Q + =S+R Q When G is a clock signal, two gated D latches comprise an edge-triggered D Flip-Flop (FF) D CLK Q if(clk is low) Q does not change else Q becomes D shortly after the rising edge Note Q s waveform is not exactly the same with D s.
36 Summary (4/8) Q + =S+R Q SR Flip-Flop (FF) Master and slave When the master receives the input and updates, the slave is close. When the slave outputs, the master does not respond to any input change.
37 Summary (5/8) Q + =S+R Q SR Flip-Flop (FF) (cont) When CLK is low, S 1 R 1 =SR P + = S+R P, master is updated S 2 R 2 =00 Q does not change
38 Summary (6/8) Q + =S+R Q SR Flip-Flop (FF) (cont) When CLK is high, S 1 R 1 =00 P does not change master does not respond to inputs S 2 R 2 =PP Q + =P+(P ) Q=P
39 Summary (7/8) Q + =S+R Q SR Flip-Flop (FF) (cont) SR P Master CLK Q low high low high low high Slave The final output, Q, was not affected by 01.
40 Summary (8/8) Q + =S+R Q JK Flip-Flop (FF) Very similar to SR master-slave Flip-Flop (FF) Except JK=11 inverts the output T Flip-Flop (FF) T=1 inverts the output T=0 keeps the same output
41 Flip-Flops (FFs) with Additional Inputs (1/3) Clear and Preset signals are two asynchronous signals and do not depend on CLK.
42 Flip-Flops (FFs) with Additional Inputs (2/3)
43 Flip-Flops (FFs) with Additional Clock enable signal Inputs (3/3)
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