18_asm.pdf

7/28/2019 18_asm.pdf

1/22

ECE124 Digital Circuits and Systems Page 1

Algorithmic state machines (ASM)

An alternative to a state diagram which is sometimes nicer when our hardware is

implementing an algorithm that can be drawn as a flowchart.

The ASM is tied closely with a hardware implementation.

The ASM consists of three types of elements:

State Box.

Decision Box.

Conditional Output Box.

7/28/2019 18_asm.pdf

2/22


ASM charts state boxes

The state box is equivalent to the state bubble in a state diagram; it represents one

state of the system.

The state can have a name, and its binary encoding.

Moore machine outputs (those outputs that depend on the current state of the

system) can be shown inside of the box.

State Name Binary Code

Moore Machine

Outputs

7/28/2019 18_asm.pdf

3/22


ASM charts decision boxes

The decision box represents a choice (conditional expression) that depends on one or

more inputs to the circuit (control unit).

ConditionalExpression

1 (true)0 (false)

7/28/2019 18_asm.pdf

4/22


ASM charts conditional output boxes

The conditional output box allows for specifying outputs that depend on both the

current state and the current inputs.

In other words, it contains Mealy outputs.

Mealy Outputs(Conditional

Outputs)

7/28/2019 18_asm.pdf

5/22


Comments

If the ASM Chart does not have any conditional output boxes, then the ASM Chart isdescribing a Moore Machine.

If the ASM chart does have conditional output boxes, then the ASM Chart is describing

a Mealy Machine.

Also, when we have outputs, we only need to label the output values (in either a state

box or a conditional box) when the outputs are 1. If not shown, we can assume the

outputs are 0.

7/28/2019 18_asm.pdf

6/22


Design steps given an ASM

Design of a clocked sequential circuit from an ASM chart is the same as from a state

diagram in so far as we start by generating a state table.

We determine the number of states from the number ofASMstate boxes.

We perform state assignment for the ASMstate boxes.

We use the ASMconditional output boxes, ASMstate boxes and ASM decision

boxes to determine output values.

We use decision boxes to determine the next state from the current state.

Of course, once we have a state table, we are pretty much go to go using what we

have talked about previously in the course.

7/28/2019 18_asm.pdf

7/22


Example design from ASM (1)

Assume we have an ASM Chart for a circuit

with three states (S0, S1 and S2), threeinputs (G, W and Z) and one output (A).

Assume state assignment has already been

performed:

S0

7/28/2019 18_asm.pdf

8/22



We can obtain our state table from the ASM Chart S0 00

A = 1

G=1 10

S1 01

W=1 10

S2 10

A = 1

Z=1 10

From here, we would proceed as normal in order to

get a circuit implementation Pick FF type, generateequations, etc

7/28/2019 18_asm.pdf

9/22



A few comments:

There is an extra arrow shown entering into S0. This is the reset signal, so S0 is

the initial state.

If an output is not explicitly shown to be assigned a non-zero value, then it isassumed that the output is 0 (I made this comment before).

7/28/2019 18_asm.pdf

10/22


One-hot encoding and ASM

ASM Charts are closely tied with hardware if we use DFF and one-hot encoding We

can go directly from an ASM Chart to a circuit!!!

Each type of box in the ASM has a direct circuit translation.

So the connections shown between different boxes in the ASM correspond to

connecting small sub-circuits together to make a larger circuit.

7/28/2019 18_asm.pdf

11/22


Circuit for an ASM state box

State Box becomes a DFF. Any specified outputs can be implemented later using

extra logic.

State Name Binary Code

Moore MachineOutputs

Entry

Exit Exit

D Q

Entry

7/28/2019 18_asm.pdf

12/22


Circuit for an ASM decision box

Decision Box becomes a few AND gates and a NOT gate

Exit0 Exit1

Entry X

X

10

Entry

Exit0 Exit1

7/28/2019 18_asm.pdf

13/22


Circuit for an ASM conditional output box

We simply tap off the signal and feed it to other circuitry to generate outputs.

X1

Entry

Exit1 Exit1

EntryX

7/28/2019 18_asm.pdf

14/22


Circuit for an ASM join

When edges join together, we can implement with an OR gate.

Entry0 Entry1

Exit

Entry0 Entry1

Exit

7/28/2019 18_asm.pdf

15/22


ASM Charts One Hot Encoding Implementation

S0 00

A = 1

G=1 10

S1 01

W=1 10

S2 10

A = 1

Z=1 10

D Q

D Q

D Q

Z

W

G

A

7/28/2019 18_asm.pdf

16/22


Design Example Shift/Multiply

Suppose we need to design a circuit that has two, n-bit inputs and one 2n-bit output.

The output is the product (multiplication) of the inputs.

We did see a combinatorial circuit for this operation the binary array multiplier.

We want to build the circuit in a different way (use only 1, n-bit adder rather than an

array of adders).

7/28/2019 18_asm.pdf

17/22



Recall how we do multiplication of binary numbers:

Multiplication is a shift and add operation.

We shift the multiplicand to the left (if multiplier bit is non-zero) and add.

7/28/2019 18_asm.pdf

18/22



Rather than shifting the multiplicand to the left and adding, consider shifting the

partial product to the right and adding:

7/28/2019 18_asm.pdf

19/22



To multiply 2, n-bit numbers we need to ADD and SHIFT n times. We can skip some

ADD operations if the multiplier bit is 0.

7/28/2019 18_asm.pdf

20/22



Design system by grabbing a bunch of functional blocks to perform necessary

operations:

n

n

n

n-bit register

q

d

multiplicand

n

n-bit shift registerq

d

n

din dout

n-bit shift registerq

ddin dout

n

n

multiplier

1-bit shift registerq

ddin dout

product

load1

n-bit addercout

sum

a b

shift

load2clear

lsb

n-1

z

controlvalid

strt

lsb

zero

ceil(log(n))

down counter

load1

lden

dec

shift

load2

load1

clear

dec

7/28/2019 18_asm.pdf

21/22



We can draw an ASM chart that generates the

correct control signals:S0clear=1load1=1

strt

1

0

load2=1

MUL0

lsb0

1

MUL1

dec=1shift=1

z1

valid=1

0

Completing the design from the ASM Chart

to a schematic for the control part of the

design is straightforward, using stuff welearnt before.

7/28/2019 18_asm.pdf

22/22



Waveforms for our 4-bit example (1001 x 1101 = 01110101):

18_asm.pdf

Documents