Lecture 12

Latches Section 5.1-5.3

Schedule3/10

Monday Latches (1) 5.1-5.3

3/12

Wednesday Flip-flops 5.4

3/13

Thursday Flip-flops, D-latch  

3/17

Monday Spring break  

3/19

Wednesday Spring break  

3/20

Thursday Spring break  

3/24

Monday Analysis of clocked sequential circuit (1) 5.5

3/26

Wednesday Analysis of clocked sequential circuit (2) 5.5

3/27

Thursday Clocked 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

Combinational Circuits

The outputs { are determined exclusively by the inputs,i.e., and .

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 Circuit Sequential 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)

Y1=xy1+x’y2

Y2=xy’1+x’y2

Maps and Transition Table (Optional Slides)

stable states: y1y2=Y1Y2

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

𝑄

𝑄

S=1 and R=1: holds the current state

S=0 and R=0

0

0

1

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

0

S=1 and R=0:

The outputs (and )are complementary.

S=0 and R=1

0

1

0

1

S=0 and R=1:

The outputs (and )are complementary.

Observations

0

1

0

1

S=0 and R=1:

1

0

1

0

S=1 and R=0:

Use active low inputs (i.e. logic “0”) to produce changesat 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 Rgoes 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 Sgoes back to 1.

Symbol of the NAND based SR latch

Active lowinputs

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’

Comparison

D Latch(An Improvement Over SR Latch)

D 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.

D-latch Operation

Verilog

Outline

• Continuous Assignment• Procedural statement– Blocking statement– Non-blocking statement

Continuous Statement

The updating of a continuous statement is triggered wheneverthere 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.

Verilog Model of a D Latch

Partial Listing of a Verilog Test Bench

Output