# Lecture 14: State Tables, Diagrams, Latches, and Flip Flop

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1 EE210: Switching Systems Lecture 14: State Tables, Diagrams, Latches, and Flip Flop Prof. YingLi Tian Nov. 6, 2017 Department of Electrical Engineering The City College of New York The City University of New York (CUNY) 1

2 What we learn so far Basic Design Combinational Systems (have no memory ) Outputs are only function of current input combination Nothing is known about past events Repeating a sequence of inputs always gives the same output sequence Now Sequential Systems (have memory) Repeating a sequence of inputs can result in an entirely different output sequence 2

3 Sequential Systems Combinational logic + memory devices System inputs Memory contents (data & addresses) System outputs Memory updates 3

4 Clocked (Synchronous) System Example of clock signal: T length of one cycle 1/T frequency ( 200 MHz -- T = 5 nanoseconds) Leading-edge and Trailing-edge Differences of these two signals? 4

5 Definitions of State Tables and Diagrams - 1 A State is a particular set of instructions which will be executed in response to the machine's input. A State Table shows, for each input combination and each state, what the output is and what the next state is. A State Diagram (state graph): a graphical representation of the state table. Timing trace: a set of values for the input and output (and sometimes the state or other variables of the system, as well) at consecutive clock times. 5

6 Definitions of State Tables and Diagrams - 2 Present State is the current state stored in memory. Next State is what will be stored in memory after this clock transition. Present output: Moore model -- output depends only on the present state of the system (not the present input). Mealy model output depends on both the present state and the present input. 6

7 State Table and Diagram (Moore model) A system with one input x and one output z such that z=1 if and only if x has been 1 for at least three consecutive clock time. possible clock transitions present state output q is the present state:

8 State Table and Diagram (Mealy Model) A system with one input x and one output z such that z=1 if and only if x = 1 and has been 1 for at least two consecutive clock time. present state input output 1 Wrong in the textbook

9 Latches A latch is a binary storage device with feedback. SR NOR latch: Set P = (S + Q) Q = (R + P) S and R are active high (Q ) If S = 0, R= 0, then P = Q & Q = P (hold) Reset If S = 1, R= 0, then P = 0 & Q = 1 (store a 1 in the latch, on line Q) If S = 0, R= 1, then P = 1 & Q = 0 (Reset the latch to store a 0 on line Q) If S = 1, R= 1, then P = 0 & Q = 0 (the latch is not operated, forbidden state) 9

10 SR NAND Latch indicate active low If = 0, = 1, then Q = 1 (store a 1 in the latch, on line Q) If = 1, = 0, then Q = 0 (Reset the latch to store a 0 on line Q) If = 1, = 1 (hold) If = 0, = 0 (forbidden state) 10

11 A Gated Latch Adding a second level of AND gates to a SR latch. Enable signal When gate signal = 0 (disable), the latch remains unchanged (hold). When gate signal = 1 (enable), the latch acts at a SR latch. 11

12 Flip Flops A flip flop is a clocked binary storage device that stores either a 0 or a 1. Must have a clock signal (trigger). Leading-edge triggered Trailing-edge triggered Types of Flip Flops: D flip flops SR flip flops T flip flops JK flip flops 12

13 D (data or delay) Flip Flops D flip flop performs as its output Q looks like a delay of input D. The Q output takes on the state of the D input at the moment of a positive edge at the clock pin (or negative edge if the clock input is active low). It is called the D flipflop for this reason, since the output takes the value of the D input or data input, and delays it by one clock cycle. 13

14 D (data or delay) Flip Flops q* = D The output depends only on the input. The D flip flop behavior table: State and output 14

15 A Trailing-edge Triggered D Flip Flop outputs?? The changes of D between a clock transition will not change output. 15

16 A Leading-edge Triggered D Flip Flop Summary: 1. Q = D (output depends only on the input value at the triggered edges but with a slight delay). 2. The output will not change if the input D changes between a clock period (non triggered edge part) 16

17 Announcement HW5 is due today, HW6 is out today, due on 11/13/2017 Read Chapter 6.1, 6.2 Next class (Chapter 6.3): Flip Flops 17

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