Chapter5: Synchronous Sequential Logic – Part 1 Origionally By Reham S. Al-Majed Imam Muhammad Bin Saud University

Outline Introduction. Sequential Circuits Latches Flip flops Types of SC. Latches Flip flops SR FF. D FF. JK FF. T FF.

Introduction The circuits considered thus far have been combinational The output depends only on the current inputs. Most systems in practice include storage elements. Sequential logic.

Sequential Circuits It consists of: Combinational circuit. Storages element. Storage elements are devices capable of storing binary information. The binary information stored in these elements at any given time defines the state of the SC at that time.

Sequential Circuits The SC receives binary information from: External input. Present/Current state of storage element. The next state in the storage element is a function of: Present/Current state. The SC is specified by a time sequence of inputs, outputs, and internal states. Current State Next State

Sequential Circuits Two main types of SC according to the timing of their signals: Synchronous SC: The activity within the circuit and the resulting updating of stored values is synchronized to the occurrence of clock pulses. Asynchronous SC: Depends upon the input signals at any instant of time and the order in which the inputs change. Difficult to design.

Synchronous Sequential Circuits Synchronization is by timing device called clock generator  clock signal (denoted by clock or clk) periodic train of clock pulses. Storage elements are affected only with the arrival of each pulse. In clocked SC: The clock signal determine when changes will occur. The other signals (e.g. inputs ) determine what are the changes that affect storage elements.

Clock Signal A sequence of 1s and 0s (ON and OFF periods) Positive edge Transition (rising edge) Positive pulses/level 1 Negative edge Transition (falling edge) Negative pulses/level

Storage Element / Memory

Storage Element A memory should support at least three operations. What exactly is memory ? A memory should support at least three operations. It should be able to hold a value. We should be able to read the value that is saved. We should be able to change that value.

One Bit Storage Elements It should be able to hold a single bit, 0 or 1. We should be able to read the bit that is saved. We should be able to change the bit. can set the bit to 1 can reset or clear the bit to 0.

Storage Element The momentary change in the storage element state is called a trigger. Two types of triggering: Pulse-triggered (Level-Sensitive) Edge-triggered Positive edge-triggered (from 0 to 1) Negative edge-triggered (from 1 to 0) Main difference between storage elements: Number of inputs they have. How the inputs affect the binary state.

Storage Element Two main types of storage elements: Latches Flip-Flops Operate with signal levels. Called level-sensitive. Not practical for use in synchronous sequential circuits Flip-Flops Controlled by clock transition. Called edge-sensitive. Flip-Flips are built with latches Used in clocked SC.

Latches

Latches A latch is binary storage element Can store a 0 or 1 It is the most basic storage element. It is easy to build. The trigger of a latch start as soon as the clock pulse changes to the logic-1 level. The new state of a latch appears at the output while the pulse is still active. Latches respond to new input values as clock pulse is still at logic-1 level.

Latches Types SR Latch ŚŔ Latch Clocked SR Latch D Latch Latch with Set and Reset inputs implemented with NOR gates ŚŔ Latch Same as SR latch except it is implemented with NAND gates Clocked SR Latch SR with additional control input (clock) D Latch An enhanced storage element from SR Latch with Data input

1- Basic S-R Latches Two input S(set) R(rest) and Two output Q and Q’ The S-R latch input will let us control the outputs Q and Q’. Q and Q’ feed back into the circuit, so they’re not only outputs, they’re also inputs! To figure out how Q and Q’ change, we must look at not only the inputs S and R, but also the current values of Q and Q’. Q next = (R + Q’current)’ Q’next = (S + Qcurrent)’

1- What if S = 0 and R = 0 The equations on the right reduce to: Q next= (0 + Q’ current)’= Q current Q’ next= (0 + Q current)’= Q’ current So when SR = 00, then Qnext= Qcurrent. This is exactly what we need to store values in the latch.

1- Resetting the latch: SR = 01 Since R = 1, Qnext is 0, regardless of Qcurrent. Qnext= (1 + Q’current)’ = 0 Then this new value of Q goes into the bottom NOR gate, where S = 0. Q’next= (0 + 0)’ = 1 So when SR = 01, then Q next= 0 and Q’next= 1. This is how you reset, or clear, the latch to 0; the R input stands for “reset.”

1- Setting the latch: SR = 10 What if S = 1 and R = 0? Since S = 1, Q’next is 0, regardless of Qcurrent. Q’next= (1 + Qcurrent)’ = 0 Then this new value of Q’ goes into the top NOR gate, along with R = 0. Qnext= (0 + 0)’ = 1 So when SR = 10, then Q’next= 0 and Qnext= 1. This is how we set the latch to 1; the S input stands for “set.”

1- SR latches are memories! This characteristic table shows that our latch provides everything we need in a memory: we can set it, reset it, or keep the current value. The output Q represents the data stored in the latch. It is also called the state of the latch. We can expand the table above into a state table, which explicitly shows that the next values of Q and Q’ depend on their current values, as well as on the inputs S and R.

1- What about SR = 11? Both Q next and Q’ next would become 0, which contradicts the assumption that Q and Q’ are always complements. SR =11 is avoided

1- SR Latches

2- S’ R’ Latches (SR Latch with NAND Gate) Similar to SR latch ( but it is complemented) Two states: Reset (Q = 0; Q`=1) and set (Q = 1; Q`=0) When S=R=1, Q remains the same S=R=0 is not allowed!

3- SR Latch with Clock The basic SR latch with an additional control input (clock) determines when the state of the latch can be changed.

3- SR Latch with Clock It consists of the basic SR latch with two additional NAND gates. The control input C acts as an enable signal to the latch When C=0, the S and R inputs have no effect on the latch, so the latch will remain in the same state regardless of the values of S and R. When C=1, the S and R inputs will have the same effect as in the basic SR latch

4- D Latch One way to eliminate the undesirable undefined state in the SR latch is to ensure that the inputs S and R are never equal to 1 at the same time.

4- D Latch Adding an inverter to the S-R Latch, gives the D Latch Ensure S and R are never equal to 1 at the same time Add inverter Only one input (D) D connects to S D’ connects to R D stands for data Output follows the input when C = 1 Transparent When C = 0, Q remains the same

Generally, Latches A latch is designated by a rectangular block with inputs on the left and outputs on the right One output designates the normal output, the other (with the bubble) designates the complement For S’R’ (SR built with NANDs), bubbles added to the input

Flip Flops

Flip-Flop The problem with the latch is that it responds to a change during a positive level (or a negative level) of a clock pulse but in a sequential circuit we need to trigger the element only at a signal transition instant.

Flip Flop

D Flip-Flop The most economical FF because it need smallest number of gates between all FF types. Two different ways to construct a D flip-flop from latches are here. Master-slave D flip-flop is shown below

D Flip-Flop Timing diagram example ( rising edge): Clock D Q

D Flip-Flop 3 SR latches 2 latches respond to the D (external input) and CLK Third will provide the output for the FF

D Flip-Flop More efficient construction (using three SR latches) CLK = 0 , S and R are equal to 1 (which causes no change in the output) CLK becomes 1: If D = 0 , R changes to 0 (Since S = 1) and this resets the flip-flop, making Q = 0 Now if D changes its value (while CLK = 1), since R = 0, it will not change the value of R. CLK becomes 0, R goes to 1 which is a normal condition (as S is still 1), causing no change in the output. CLK goes from 0 ( previous step )to 1 D = 1 when, set state.

JK Flip-Flop The indeterminate condition of the SR type is defined in the JK type. It can set/reset/complement the output. Characteristics table: Characteristics equation: Q(t+1)= JQ’+K’Q

JK Flip-Flop Timing diagram example ( rising edge): Clock J K Q

T Flip Flop ×خ

T Flip-Flop Timing diagram example ( rising edge): Clock T Q

Direct Inputs Flip Flops will sometimes provide special input terminals for setting or clearing the FF asynchronously. Direct inputs force FF to a state independently of clock. The input that sets FF to 1 is called preset or direct set. The input that resets FF to 0 is called clear or direct reset. These inputs are useful for bringing the FFs to an initial state prior to its clocked operation.

Excitation Table In the design process: We know the transition from the present state to the next state. Want to find the FF inputs that cause the transition. To achieve the goal of design we need Excitation Table. A table that lists the required inputs for a given change of state. D 1

FF Summery Three types of Flip Flop: D Flip Flop(FF) JK FF. T FF consider the basic and more efficient. Other FF can be constructed using it. 1 input (D), and can Set/Reset output. JK FF. Constructed with D FF and gates. 2 inputs (J,K) and can Set/Rest / Complement the output. T FF Constructed with D FF and XOR gate 1 input( T) and can implement the output.