 # Lecture 12 Latches Section 5.1-5.3, 9.1-9.2. Block Diagram of Sequential Circuit gates New output is dependent on the inputs and the preceding values.

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Lecture 12 Latches Section 5.1-5.3, 9.1-9.2

Block Diagram of Sequential Circuit gates New output is dependent on the inputs and the preceding values of outputs. Characteristic: the output node is intentionally connected back to inputs.

Sequential Circuits Two types of sequential circuits – Synchronous: circuits whose behavior can be defined from its signals at discrete instants of time. Clocks are to achieve synchronization. – Asynchronous circuits depend on input signals and the order in which the inputs change. (No clock pulses are used!)

Block Diagram of Sequential Circuit Sychronous circuits: Used clocked flip-flops Asychronous circuits: Use unclocked flip-flops or time delay elements

Applications of Asynchronous Circuits Asynchronous circuits are important where the digital system must respond quickly without having to wait for a clock pulse Useful in small independent circuits that require only a few components— where it may not be practical to go to the expense of providing a circuit for generating clock pulses!

A Generic Asynchronous Circuit Y n is equal to y n only in the steady state! Combinational circuit produces propagation delay (2n-10ns) The delay element produced additional 1 ns delay per foot.

Asynchronous Sequential Circuit Y 1 =xy 1 +x’y 2 Y 2 =xy’ 1 +x’y 2

Maps and Transition Table stable states: y 1 y 2 =Y 1 Y 2

Toggle x X= 0→1 → 0 → 1

Latches Latches are level sensitive. Latches propagate values from input to output continuously. S sets Q =1; R sets Q=0 – Active low inputs are enabled by 0s. – Active high inputs are enabled by 1s.

SR Latch with NOR Gates t PDSQ =2 NOR gate delays. t PDRQ_ =1 NOR gate delay Forbidden State SR are trigger pulses which can return to zero once Q is set. Active High inputs

Typical Mode of Operation 1.Both inputs of the latch remain at 0 unless the state has to be changed. 2.When both S and R are equal to 0, the latch can be in either the set or the reset, depending on which input was most recently a 1. S must go back to 0 in order to avoid S=R=1. Q and Q’ do not change states when S goes back to 0. R must go back to 0 in order to avoid S=R=1. Q and Q’ do not change states when R goes back to 0.

SR Latch with NAND Gates 1.Both inputs of the latch remain at 1 unless the state has to be changed. 2.When both S and R are equal to 1, the latch can be in either the set or the reset, depending on which input was most recently a 1. R must go back to 1 in order to avoid S=R=0. Q and Q’ do not change states when R goes back to 1. S must go back to 1 in order to avoid S=R=0. Q and Q’ do not change states when S goes back to 1.

Comparison (activated with a 1) (activated with a 0)

SR Latch with NAND Gates Active low inputs

SR latch with Control Line (En=0) 1. En=0, Q and Q’ will not be changed! 0 1 1

SR latch with Control Line (En=1) 1.En=1, Q and Q’ will be affected by S and R. 2.We now have active-high enabled circuit! 1 S’ R’

D Latch

D Latch (En=0) 0 1 1

D Latch (En=1) 1 D’ D Q follows D as long as En is asserted (En=1). Data is temporary stored when En is 0.

D-latch Operation

D-Latch (CK=0) 0 D DB 0 0

D-Latch (CK=1) 1 D DB D D

Analyze D Latch Using Boolean Algebra

Transistor Level (Optional) Implementation of D-Latch

Clock Generation Increment clkcdiv at The rising edge of mclk 0000 0001 0010 0011 0100 0101 0110 0111 1000 1001 1010 1011 Clkdiv toggles every 4 cycles Clkdiv toggles every 2 cycles. Single pass behavior Cyclic behavior Non-blocking statements

Initial keyword Single-pass behavior An initial behavior statement executes just once. Initial statement executes at the start of simulation and expires after all of its statements have completed execution. An initial statement is also a procedural statement

always always is a procedural assignment The variables in the left hand side of procedural statement must be of the reg data type. Clkdiv can not be a wire because clk is not updated until always sees positive edge of mclk. Therefore, clkc can not be a wire type.

Continuous versus Procedural Statement Procedural statement Continuous statement: Clk_out is updated whenever Clkcdiv changes. clk_out is a wire! Clkdiv is only incremented when a posedge of mclk is detected. clkdiv is a reg!

Blocking versus Nonblocking Statements There are two kinds of procedural assignments: – Blocking statements Use (=) as the assignment operator Blocking statements are executed sequentially in the order they are listed. Used to model behavior that are level sensitive (i.e. in combinational logic) – Nonblocking statements Use (<=) as the assignment operator Nonblocking statements are executed concurrently. Used to model synchronous/concurrent behavior.

Blocking Statements B=A (transfers A to B) C=B+1 (increments B and writes the value to C)

Nonblocking Statements B<=A C<=B+1 – The value of A is kept in one storage location – The value of B+1 is stored in another storage location – After all the expressions in the block are evaluated and stored, the assignment to the targets on the left-hand side is made. – C will contain the original value of B, plus 1. This is the value of B before A is written into B.

Top Level Verilog of clk_gen

Generate a Test Vector Load test vector at t=0 Set dout equal to testvector[vectornum] at the rising edge of a dclk

bit_str.txt Generate a bit file with rand() fundtion

tvector simulation

Verilog Model of d latch

Test Bench

Use a Digital Oscilloscope Generate a binary vector in matlab Load the binary vector onto the function generator

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