ECA1212 Introduction to Electrical & Electronics Engineering Chapter 9: Digital Electronics – Sequential Logic by Muhazam Mustapha, November 2011

Learning Outcome By the end of this chapter, students are expected to understand –the basic ideas about sequential logic –flip-flops and counters

Chapter Content Sequential Logic Flip-flop Flip-flop Control Counters

Sequential Logic CO3

Definition Combinational logic is a logic circuit that gives output based on an input combination and doesn’t keep any memory of the previous condition Sequential logic is the type of digital system that does not only depend on current input, but also the previous history of the system For that reason sequential logic requires memory elements to function Sequential systems also require external combinational system to make computations CO3

General Block Diagram Sequential Logic Combinational Logic Sequential System InputOutput Clock CO3

Memory Elements: Flip-flops CO3

SR Flip-Flop The NOR inputs available for controlling the value is labeled S and R because they have the effect of setting (S) and resetting (R) the output If both of the input are 1, the circuit gives invalid output S R Q Q S R Q Q SR Current Q Next Q (Q*) Invalid 11 Characteristic equation: Stay Reset Set Invalid CO3

JK Flip-Flop JK flip-flop is an extension of SR flip-flop to remove the invalid input condition The condition J=1 and K=1 (invalid in SR) is set to toggle condition – the output just inverts It can be built around SR flip-flop with some modification at the input CO3

JK Flip-Flop J K Q Q S R Q Q JKQNext Q (Q*) clk J K Characteristic equation: clk Stay Reset Set Toggle CO3

D Flip-flop The most popular flip-flop nowadays Built with inverted input JK or SR flip-flop so that the operation is always at SET condition At every clock pulse, the output just follow the input D Q Q DQQ* clk Characteristic equation: J K Q Q clk D CO3

T Flip-flop JK flip-flop with tied-up inputs Toggles if T is high, otherwise stays T Q Q TQQ* clk Characteristic equation: J K Q Q clk T CO3

Flip-Flop Control CO3

Triggering Modes Sequential logic circuit has memory elements and some combinational elements (gates) to perform computation The combinational logic will be fed either into the input of the flip-flop (D, T, J, K, S or R) or the clock input The clock can either trigger the flip-flop at its: –Positive edge – up-going edge, or –Negative edge – down-going edge Latches can either be controlled by low or high level CO3

Triggering Modes Q Q Q Q FF Q Q Q Q Level TriggeredEdge Triggered LatchFlip-flop Positive Edge Negative Edge High Level Low Level CO3

Clocking Modes If the clock inputs to the sequential system are coming from a single common source, it is called synchronous system Otherwise, if the clock can be derived from other sources, or may be changed by some combinational circuitry, the system is said to be asynchronous In modern designs, synchronous system is more popular as it is easier to design –The designer can ignore the circuits into the clock CO3

Clocking Modes Asynchronous Synchronous D Q clk D Q D Q D Q D Q D Q Common Global Clock CO3

Counters CO3

Counter Counter is a sequential circuit that keeps the number of clock pulses that it receives Every time a clock comes the binary value of the flip-flops (combined) will change to the next binary value The group of flip-flops that is combine together in a sequential circuit is what we call REGISTER The binary value that is kept in the register is what call STATE CO3

Asynchronous Binary Counter 1 bit counter can be built using a JK flip-flop that operates in toggle mode The circuit is also called frequency divider (divide-by-2 circuit) J K Q clk 1 1 frequency Frequency In Q CO3

Asynchronous Binary Counter The output frequency of the previous 1 bit counter looks like another clock frequency For that reason it also can be fed into a next flip- flop to create 2 bit asynchronous counter J K Q0Q0 clk 1 1 frequency Frequency In J K clk Q1Q1 1 1 Q0Q0 Q1Q1 CO3

Asynchronous Binary Counter Using the same approach we can further create 4 bit asynchronous binary counter by keep feeding 1 output of a flip-flop to the next one This type of counter is also called ripple counter J K Q0Q0 clk 1 1 Clk J K clk Q1Q1 1 1 Q0Q0 Q1Q1 J K Q2Q2 1 1 J K Q3Q3 1 1 Q2Q2 Q3Q3 CO3