程序代写代做代考 Microsoft PowerPoint - 048-caring-and-glue-logic

Microsoft PowerPoint – 048-caring-and-glue-logic

9/12/2016

University of Illinois at Urbana-Champaign
Dept. of Electrical and Computer Engineering

ECE 120: Introduction to Computing

Caring About Don’t Cares
and Glue Logic

Let’s Have Some Ice Cream!

Let’s build
something.
Anyone like
ice cream?
Let’s build
an ice cream
dispenser.
Mango and
pistachio!

Start by Specifying the Inputs and Outputs

inputs: three buttons
◦M(ango): 1 when it’s pushed
◦B(lend): 1 when it’s pushed
◦P(istachio): 1 when it’s pushed

outputs: two 2-bit unsigned numbers
◦CM[1:0]: number of ½ cups of mango
◦CP[1:0]: number of ½ cups of pistachio

The User Has Three Choices (and One Non-Choice)

Help fill in the truth
table…
Push M, get one cup
of mango.
Push B, get ½ cup of
each.
Push P, get one cup
of pistachio.
Push nothing, get
nothing.

M B P CM CP
0 0 0
0 0 1
0 1 0
0 1 1
1 0 0
1 0 1
1 1 0
1 1 1

10 00

01 01

00 10

00 00

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Fill the Rest with Don’t Cares

What about the rest?
Who cares?
Fill with x’s.

M B P CM CP
0 0 0 00 00
0 0 1 00 10
0 1 0 01 01
0 1 1
1 0 0 10 00
1 0 1
1 1 0
1 1 1

xx xx

xx xx
xx xx
xx xx

We Need to Solve for Each Output Bit

Now we can copy
to K-maps. First, CM[1].

CM[1] = M

M B P CM CP
0 0 0 00 00
0 0 1 00 10
0 1 0 01 01
0 1 1 xx xx
1 0 0 10 00
1 0 1 xx xx
1 1 0 xx xx
1 1 1 xx xx

CM[1]
BP

00 01 11 10

M
0

x0 00

1 xxx

Solve the Low Bit of Mango

Next, CM[0].

CM[0] = B

M B P CM CP
0 0 0 00 00
0 0 1 00 10
0 1 0 01 01
0 1 1 xx xx
1 0 0 10 00
1 0 1 xx xx
1 1 0 xx xx
1 1 1 xx xx

CM[0]
BP

00 01 11 10

M
0

x0 10

0 xxx

Solve the High Bit of Pistachio

And CP[1].

CP[1] = P

M B P CM CP
0 0 0 00 00
0 0 1 00 10
0 1 0 01 01
0 1 1 xx xx
1 0 0 10 00
1 0 1 xx xx
1 1 0 xx xx
1 1 1 xx xx

CP[1]
BP

00 01 11 10

M
0

x0 01

0 xxx

9/12/2016

Solve the Low Bit of Pistachio

And, finally, CP[0].

CP[0] = B

M B P CM CP
0 0 0 00 00
0 0 1 00 10
0 1 0 01 01
0 1 1 xx xx
1 0 0 10 00
1 0 1 xx xx
1 1 0 xx xx
1 1 1 xx xx

CP[0]
BP

00 01 11 10

M
0

x0 10

0 xxx

The Solution Requires No Gates!

The don’t cares made the functions so simple
that we don’t even need any gates!

CM[1]
CM[0]

CP[1]
CP[0]

What if a User Pushes Two Buttons?

Let’s be careful.
What happens if a user presses
M and B at the same time?
1.5 cups of
mango

AND
0.5 cups of
pistachio!

CM[1]
CM[0]

CP[1]
CP[0]

Don’t Cares: Not for Human Behavior!

In the best case, the cup overflows
(2 cups of ice cream instead of 1 cup).
In the worst case,
◦ the engineer of the mechanical system
◦assumed that we would not send 11, and
◦ something worse happens when we do.
So we DO care.
Generally, using don’t cares when humans
are involved is a bad idea.

9/12/2016

Let’s Clean Up the Inputs

How can we fix the problem?
One approach:
◦choose specific outputs
for each combination of inputs,

◦ then solve the K-maps again.
Another approach:
◦ clean up the inputs with more logic
◦prevent humans from ever
producing bad combinations.

Use Glue Logic to Ensure that Assumptions Hold

For example, we can force all inputs to
zero if the human presses more than one
button.
Each of the AND
gates produces
a 1 iff the
corresponding
button is the
ONLY 1 entered.

CM[1]
CM[0]

CP[1]
CP[0]

glue logic (dashed box)

The Inputs Can be Cleaned Up in Many Ways

Forcing invalid input combinations to zero
is just one strategy.
We could also choose a priority on the buttons
(six possible choices).
For example:
◦Pistachio overrides other buttons, and
◦Mango overrides Blend.

Or use a combination of approaches.

What About Picking Specific K-Maps?

In the case of our ice cream dispenser and the
strategy shown, the two approaches are the
same (just remove the dashed box!).
In general, however,
◦ these approaches vary
◦ in area, speed, and/or power.

Cleaning up the inputs is perhaps
easier to understand.

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