Schedule 3/10MondayLatches (1)5.1-5.3 3/12WednesdayFlip-flops5.4 3/13ThursdayFlip-flops, D-latch 3/17MondaySpring break 3/19WednesdaySpring break 3/20ThursdaySpring break 3/24MondayAnalysis of clocked sequential circuit (1)5.5 3/26WednesdayAnalysis of clocked sequential circuit (2)5.5 3/27ThursdayClocked sequential circuit Please bring a functional random number generator to class on Thursday (3/13).
Outline A brief overview of sequential circuits Memory elements – NAND based SR latch – NAND based D latch Verilog Modeling
Block Diagram of Sequential Circuit New output is dependent on the inputs and the preceding states of the circuit stored in the memory. Characteristic: the output node is intentionally connected back to inputs of combinational circuits.
Combinational Vs. Sequential Circuits Combinational CircuitSequential Circuit
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 Revise
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!
Asynchronous Sequential Circuit (Optional Slides) Y 1 =xy 1 +x’y 2 Y 2 =xy’ 1 +x’y 2
Maps and Transition Table (Optional Slides) stable states: y 1 y 2 =Y 1 Y 2
Toggle x (Optional Slides) X= 0→1 → 0 → 1
Memory Storage Elements
Latches Latches are level sensitive. Latches propagate values from input to output continuously. Inputs – Active low inputs are enabled by 0s. – Active high inputs are enabled by 1s.
S=1 and R=1 1 1 S=1 and R=1: holds the current state
S=0 and R=0 0 0 1 S=0 and R=0: The outputs are not complementary. This is not a state we want to be in.
S=1 and R=0 1 0 1 S=1 and R=0:
S=0 and R=1 0 1 0 S=0 and R=1:
Observations 0 1 0 S=0 and R=1: 1 0 1 S=1 and R=0: Use active low inputs (i.e. logic “0”) to produce changes at the outputs.
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 (the hold mode) 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 (the hold mode) in order to avoid S=R=0. Q and Q’ do not change states when S goes back to 1.
Symbol of the NAND based SR latch 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 (An Improvement Over SR Latch)
D Latch (En=0) 0 1 1 (hold mode)
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 disabled.
Continuous Statement The updating of a continuous statement is triggered whenever there is a change on the right hand side of the equation. The assign keyword is used is used.
Procedural Statements Procedural statements are executed when the condition is met. – Usually the condition is implemented with initial and always statements. – There are two types of procedural statements: blocking and non-blocking statements. – The left-hand side of the procedural statements must be the reg data type.
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 Non-blocking 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)
Non-blocking 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.
Example of a Non-blocking Statements X,Y, vectornum are updated concurrently.