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Digital Electronics

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Chapter 5 Synchronous Sequential Logic

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SR NAND Latch Set up the Truth Table

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SR NAND Latch Truth Table

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SR NOR Latch Set up the Truth Table

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SR NOR Latch Truth Table

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D Latch Eliminates the indeterminate S=R=1 state of the NAND Latch in addition to a control input C.

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Graphic Symbols for Latches Note: 74LS75 is D Latch

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Flip-Flops Flip-Flops are triggered by a clock transition in order to make the operation reliable Latch FF

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Master-Slave D Flip-Flop Master reads while the clock is high but Q records the last data when the clock is low.

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Positive Edge-Triggered D Flip-Flop

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Graphic Symbol for 74LS74 Edge-triggered design is superior to master- slave because reading and recording occur in a flash during the clock transition.

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T Flip-Flop Determine the Truth Table of the T FF

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D Flip-Flop and T Flip-Flop Characteristic Tables D Flip-Flop T Flip-Flop D Q(t+1) T Q(t+1) 0 0 0 No Change 1 1 1 Toggles

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Frequency Divider T Flip-Flop can be used to divide the frequency of a clock by 2. Sketch the circuit. How can you divide the frequency by 4?

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JK Flip-Flop Draw the Characteristic Table

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JK Flip-Flop J K Q(t+1) 0 0 No Change 0 1 0 (reset) 1 0 1(set) 1 1 Toggles

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JK Flip-Flop Equation Q(t+1) = JQ' + K'Q 74LS76

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What’s wrong with this picture?

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Connect a wire fom the AND gate to the D Flip-Flop. P.S. This is figure 5-15 in your textbook! P.P.S. Analyze the given sequential circuit. In other words, write the equations for A(t+1), B(t+1), and y, draw a state table, and sketch a state diagram.

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State Equations A(t+1) = A x + B x B(t+1) = A' x y = (A + B) x'

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State Table Present State Next State Output x = 0 x =1 x = 0 x =1 A B A B A B y y 00 00 01 0 0 01 00 11 1 0 10 00 10 1 0 11 00 10 1 0

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State Diagram

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Design of Sequential Circuits Design a circuit that detects three or more consecutive 1’s in a string of bits coming through an input line

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Planning, Planning, Planning! Our circuit should start off in a “state” S(0). If a 0 comes along it should stay put in S(0). If a 1 comes along it should jump to state S(1). Now if a 0 comes along it should go right back to S(0) but if a second 1 comes along it should jump to S(2). At this point if a third 1 comes along it should jump to S(3) and also set a flag. Otherwise start all over again in S(0).

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State Diagram for Sequence Detector

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Present State Next State Output x = 0 x =1 x = 0 x =1 A B A B A B y y 00 00 01 0 0 01 00 10 0 0 10 00 11 0 0 11 00 11 1 1 State Table for Sequence Detector

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K-Map for D A of Sequence Detector

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K-Map for D B of Sequence Detector

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K-Map for y of Sequence Detector

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Logic Diagram of Sequence Detector

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Some Terminology... FSM:A Sequential Circuit is also called a Finite State Machine (FSM) Mealy Model: The output (y) of an FSM depends on the input (x) as well as the present state of A and B [e.g. Fig 5-15 where y = (A+B)x'] Moore Model: The output (y) of an FSM depends on the present state of A and B but not on the input (x). [e.g. Sequence Detector where y = AB]

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// Functional description of JK flip-flop module My_JKFlipFlop (J,K,CLK,Q,Qnot); output Q,Qnot; input J,K,CLK; reg Q; assign Qnot = ~ Q ; always @ (posedge CLK) case ({J,K}) 2'b00: Q = Q; 2'b01: Q = 1'b0; 2'b10: Q = 1'b1; 2'b11: Q = ~ Q; endcase endmodule VHDL for JK Flip-Flop

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That’s All Folks!

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