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11-1 Sequential logic circuits 1. A combinational circuit and a memory component 2. the output depends not only on the present input but also on the past sequence of inputs.

11-2 Figure 11.1 Feedback feedback means that the output is connected back into the input gate in the Circuit so as to form a closed loop. The output will continue to oscillate back and forth between 0 and 1.

11-3 Figure 11.2 Stable state

11-4 Memory devices in logic circuits 1. Latch( 閂鎖 ) 除非輸入信號送出來指示要切換狀態為止，該儲存元件可以 無限期地維持原先的狀態 SR latches D latches 2. Flip-Flop( 正反器 ) Edge-Triggered flip-flop ( 邊緣觸發型的記憶單元 ) Master slave flip-flop Edge-triggered flip-flop 3. RAM and ROM—A mass memory element

11-5 Figure 11.3 Set-Reset Latch (SR Latch) What is Latch? ( 閂 : stable state ) 1.We restrict the inputs so that R=S=1 is not allowed, so the outputs P and Q always complement: P=Q’ 2.An input S=1 sets the output to Q=1, and an input R=1 resets the output to Q=0

11-6 Figure 11.5 S-R Latch The circuit and the symbol of a S-R Latch Note that the symbol: Q directly above the S input

©2010 Cengage Learning Engineering. All Rights Reserved.11-7 Figure 11.6 Improper S-R Latch Operation Note that when S=R=1, the Latch will not operate properly When S and R are both 1, P and Q are both 0. Therefore P is not equal to Q’. This violate a basic rule of latch operation that requires the latch output to complement.

©2010 Cengage Learning Engineering. All Rights Reserved.11-8 SR Latch ：由一對 NOR 閘所構成之 SR 閂鎖器，兩個互補輸出 分為兩種狀態 –S=1, R=0  set state (Q 會變成 1) –S=0, R=1  reset state (Q 會變成 0) –S=0, R=0  保持目前的值 The SR Latch

11-9 Figure 11.7 Timing Diagram for S-R Latch The timing diagram for S-R latch If the S or R input pulse is less than , the gate output will not change and the latch will Not change state.

11-10 Table 11.1 S-R Latch Next State and Output Present state and next state in a Latch Next state equation

11-11 Figure 11.8 Derivation of Q+ for an S-R Latch From the K-map When S=1, next state is 1 R=0, Q=1, next state is 1

11-12 Figure 11.9 Switch Debouncing with an S-R Latch Where the S-R latch will be used in logic circuit? 1.In asynchronous system( 非同步循序電路, ex: 儲存二進位資訊 ) 2.Debouncing switches.

11-13 Figure 11.10 S-R Latch An alternative form of S-R latch uses NAND gates. SR latch with NOR gates SR latch with NAND gates

11-14 Figure 11.11 Gated D Latch The gated D Latch 1.This type of latch is referred to as a transparent latch: because when G=1, the Q output is same as D input. Someone called this G input as a control line. Present state Input data Next state

11-15 Figure 11.13 D Flip-Flops D Flip-Flop(FF) 1.D-Latch 和 D Flip-Flop 皆為僅有一輸入端 (D) 的雙穩態記憶電路 (Q,Q’) ，常用在資料儲存 與暫存器的使用。兩種元件都能將 D 之輸入端直接傳送到記憶體的輸出，但傳送的方式 不同 : a. FF: 由一個時序脈波 (Clock, Ck; a plus generator) 之邊緣輸入訊號 (edge- triggered signal) 來決定 D 輸出。 b. Latch: 當一個適當的邏輯準位加在致能端 (Enable input, G) ，則輸入之訊號變化 (D) 均會被傳送到輸出端。

©2010 Cengage Learning Engineering. All Rights Reserved.11-16 Figure 11.14 Timing for D Flip- Flop (Falling-Edge Trigger) D FF with Falling-Edge Trigger( 負緣觸發 ) 沒有被傳遞的訊號 : 不在觸發時發生變化

11-17 Figure 11.15 D Flip-Flop (Rising-Edge Trigger) D FF with Rising-Edge Trigger( 正緣觸發 ) G2 觸發 (Q fow P) G1 不觸發 (D stored, P unchanged) G2 不 觸發 ( P stored, and Q unchanged) G1 觸發 (P fow D) G2 觸發 (Q fow P) G1 不觸發 (D stored, P unchanged) A rising-edge Triggered D-FF can be made by two gated D latches and one invertors

©2010 Cengage Learning Engineering. All Rights Reserved.11-18 Figure 11.16 Setup and Hold Times for an Edge-Trimmed D Flip-Flop A flip-flop changes state only on the active edge of the clock. To function properly, the rule are: 1.Before active edge, the D must stable for a setup time(t su ) 2.After active edge, the D must stable for a hold time(t h ) 3.The propagation delay(t p ) from the time the clock changed.

11-19 Figure 11.17 Determination of Minimum Clock Period To determine the minimum clock period 1.Suppose the invertor have 2ns delay, and FF have 5ns delay. 2.Suppose the setup time is 3ns. Ck period 7ns Ck period 15ns Ck period 10ns

11-20 Figure 11.18 S-R Flip-Flop SR Flip-Flop 1.Similar to an S-R Latch in that S=1 set Q output to 1; and R=1 resets the output to 0. The difference is that FF has a clock(Ck) input, the Q can change only after an active clock edge. 2. The truth table and next state equation(characteristic equation) is same as Latch.

11-21 Figure 11.19 S-R Flip-Flop Implementation and Timing SR Flip-Flop The circuit can be made from two SR-latch and gates.(A master-slave FF) 1.When Ck is 0: S, R set the output of the Master, while the Slave hold the previous value of Q 2.When Ck from 0 to 1: P is held in the Master and this value is transferred to the Slave 3. When Ck from 1 to 0: The Q is latched in the slave and Master can process new inputs. Change inputs When Ck is low. 1. S=1 and R=0, P=1 2. When S change to 0 at t5, but P don’t change to 0. so Q change to 1 at t5. This is incorrect! (S=R=0, no change) Change input when Ck High To avoid this incorrect!!

11-22 Figure 11.20 J-K Flip-Flop (Q Changes on the Rising Edge) J-K Flip-Flop 1. 與 SR FF 相似，主要差別在於， SR FF 在兩個輸入端皆為 1 時，會發生不確定之輸出， 而 J-K FF 的輸出狀態會反相，可以消除 SR FF 的不確定狀態。 2. 三個 inputs: Ck, J, K S RS R 1 0 0 1 1 1

11-23 Figure 11.21 Master Slave J-K Flip-Flop (Q Changes on Rising Edge) J-K Flip-Flop circuit JK FF 一般以兩 SR Latch 和 gate 連結，以 master-slave 架構來實現 1. 與 SR FF 電路相似，差別僅在於把 input S,R 換成 J, K. 且 output 需 feedback 到 input gate. 2. S= JQ’Ck’ and R=KQCk’

11-24 Figure 11.22 T Flip-Flop T Flip-Flop: 1. Also called a toggle FF, is frequently used in building counters. 2. Can be programmed in CPLDs and FPGA. 3. when T=0, no state change at Ck active edge when T=1, state change at Ck active edge

11-25 Figure 11.23 Timing Diagram for T Flip-Flop (Falling Edge Trigger) The Timing diagram for a T-FF

11-26 Figure 11.24 Implementation of T Flip-Flops Implement a T-FF circuit Connect the J,K inputs. J-K FF D FF

11-27 Figure 11.25 D Flip-Flop with Clear and Preset Filp-Flop with Additional Inputs 1.Can be used to set the FF to an initial state independent of the clock. 2.ClrN: Clear Notation 3.PreN: Present Notation Note the inverter, so ClrN and PreN is active-low( 低準位觸發反應 ) 1. 當 PreN, ClrN 皆為 0 ，不允許 2. 當 PreN 為 0, 不管其他如何, output 強制設置為 1 3. 當 ClrN 為 0, 不管其他如何, output 強制歸為 0. 4. 當 PreN 和 ClrN 皆為 1, 依循 D-FF 原本 之操作 : 在 Ck 產生邊緣觸發時，傳送 D 至 output.

11-28 Figure 11.26 Timing Diagram for D Flip-Flop with Asynchronous Clear and Preset The timming Diagram for a D-FF with ClrN and PreN 由於 ClrN =0 強制 Q 為 0 ( 雖然在 Ck rising-edge) 過程中 ClrN 回到 1 兩者皆為 1 ，因此回到原本操作 在下一個 Ck rising edge 觸發點, 看 D 輸出 D 此時變 0 由於 PreN =0 強制 Q 為 1 過程中 PreN 回到 1 兩者皆為 1 ，因此回到原本操作 在下一個 Ck rising edge 觸發點, 看 D 輸出

11-29 Figure 11.27 D Flip-Flop with Clock Enable Common Clock 1.In a synchronous digital system( 同步數位系統 ), the FFs are usually driven by a common clock. 2. 以下兩種方式可以實現這樣電路 : a. Gating the clock: 存在一個潛在問題，當並接多個 FFs 的同步電路，因為 gate delay 的問題，導致實際傳達到每個 FF 的時間不同步。 b. D clock-enable( D-CE): 可以解決上述的 gate delay 問題，且這樣的電路常使用在 CPLDs 和 FPGA 電路設計中。當 CE=0, Ck 變成 disabled, output 維持不變 ; 當 CE=1, 元件操作為一個典型的 D-FF, Q=D. 所以 characteristic equation : 可以由一 MUX 來實現

11-30 Summary 1.SR latch and SR-FF 2.Gated D latch and D-FF 3.D-CE FF 4.JK-FF 5.T-FF Note that JK-FF and D-FF can convert to a T-FF The next-state (characteristic)equations:

11-31 循序電路的設計法 狀態圖 ( 以二進制計數器為例 ) 狀態表 輸入表

11-32 K-map 邏輯電路