1 Fundamentals of Computer Science Sequential Circuits

2 What is a Sequential Circuit? A sequential circuit consists of logic gates whose output(s) at any time are based on the values of external input(s) and internally generated input(s). Sequential circuits are used to implement storage elements. Sequential Circuit inputs outputs

3 What is a Sequential Circuit? Sequential circuits are generally part of a larger circuit that contains combinational circuitry as well. There are two types of sequential circuits –Synchronous sequential circuits can only be affected at discrete instances of time. They are driven by clock generators. When a clock pulse is absent, the circuit cannot change. –Asynchronous sequential circuits can be affected at any instances of time. They are not clock driven.

4 Synchronous Sequential Circuits Flip-flops are a type of synchronous sequential circuit. Each flip-flop can store 1-bit of data.

5 Asynchronous Sequential Circuits Latches are a type sequential circuit that may be asynchronous or synchronous. Each latch can store 1-bit of data.

6 Unstable Asynchronous Sequential Circuit This is an example of a simplest-case sequential circuit. –The circuit is built from a single inverter. –The output oscillates rapidly between 0 and 1. –The circuit is essentially useless.

7 Stable Asynchronous Sequential Circuits When the circuit settles down, the two outputs will be the complement of each other. There is no way to modify the value stored in the circuit. The circuit is essentially useless.

8 Latches Latches are the most basic storage element. Latches are used to build flip-flops. This SR latch is a type of asynchronous sequential circuit.

9 Logic Simulation of SR Latch Behavior

10 SR Latch with NAND Gates The input signals for the NAND latch are the complement of the signals for the NOR latch, hence the name SR latch.

11 SR Latch with Control Input Latch can only change when C = 1, all other times the circuit remains in the same state no matter what values are on the S and R inputs. This SR latch is a type of synchronous sequential circuit.

12 D Latch with Control Input The D latch is designed to eliminate the undefined state by ensuring that the S and R inputs are never high at the same time.

13 Flip Flops A latch is transparent. –Its input value can be seen directly from its output value. Which is to say that the outputs respond immediately to the inputs. –This is the case with the D latch when its control, C, is high. Flip-flops avoid the transparency problem by providing a “disconnect” between the inputs to the flip-flop and the outputs from the flip-flop.

14 Flip Flops Imagine the following scenario. –The clock goes high. –The output of the D latch, Q, responds to the input, D. –Before the clock goes low, the new value of Q filters through the combinational circuit and into the D latch changing the value of Q for the second time during the same clock cycle.

15 SR Master-Slave Flip-Flop A flip-flop contains two clock-driven latches. –The first flip-flop is the master. –The second flip-flop is the slave. The slave receives the inverse of the clock signal received by the master.

16 SR Master-Slave Flip-Flop When the master’s clock input is high (and the slave’s is low) the slave is impervious to change so the slave’s outputs become stable. When the master’s clock is low (and the slave’s is high) the slave will respond to the master’s outputs. –During this time the master’s outputs will remain stable since the master’s clock is low.

17 Logic Simulation of SR Master-Slave Flip-Flop

18 JK Master-Slave Flip-Flop The master-slave JK flip-flop is designed to eliminate the undefined condition (both S and R are high) found in SR latches. When both J and K are high, the value of the flip-flop toggles.

19 Flip-Flop Characteristic Tables

20 Base 4 Binary Counter with Enable A base 4 binary counter with enable repeatedly outputs the bit pattern 00, 01, 10, 11 when ever the enable line is high. –Since the circuit is clock driven (synchronous), the count will change when ever the clock goes from high to low. –When the enable line is low, the counter stops counting and the output value remain constant. The counter must “remember” what the current count is so that it knows what value to output next.

21 Base 4 Binary Counter with Enable The next state of the circuit is based on the current state and the value of the enable line. –The current state of the counter is stored in two flip-flops, one per binary digit. A state table is used to show what the next state of the circuit will be relative to the current state and any external inputs. –State tables are used in sequential circuit design much as truth tables are used in combinational circuit design.

22 Base 4 Binary Counter with Enable Counter Enable DADA DBDB

23 Base 4 Binary Counter with Enable