程序代写代做代考 Microsoft PowerPoint – 047-dont-cares
Microsoft PowerPoint – 047-dont-cares
9/12/2016
University of Illinois at Urbana-Champaign
Dept. of Electrical and Computer Engineering
ECE 120: Introduction to Computing
Don’t Care Outputs
ECE 120: Introduction to Computing © 2016 Steven S. Lumetta. All rights reserved. slide 1
Some Input Combinations May Not Matter
ECE 120: Introduction to Computing © 2016 Steven S. Lumetta. All rights reserved. slide 2
Sometimes, we don’t care whether a particular
input combination generates a 0 or a 1.
For example,
◦when an input combination is
impossible to generate, or
◦when outputs are ignored in the
case of an input combination.
For Such Inputs, Use ‘x’ to Indicate “Don’t Care”
ECE 120: Introduction to Computing © 2016 Steven S. Lumetta. All rights reserved. slide 3
In such cases, we use ‘x’ (called a
“don’t care”) in place of the desired output.
Indicates that either 0 or 1 is acceptable.
However: whatever we implement will
generate a 0 or a 1, not a “don’t care.”
So we need to be sure that we really do not
care.
Why Are “Don’t’ Cares” Useful?
ECE 120: Introduction to Computing © 2016 Steven S. Lumetta. All rights reserved. slide 4
More choices often means a “better”
answer (for any choice of metric).
Say that you optimize a K-map
for a function F.
Then you consider several other
functions G, H, and J.
If you have to pick one of the four functions
(F, G, H, or J), the choice can’t get worse,
since you can always pick F, but the best
choice may be better than F.
9/12/2016
N “Don’t Cares” Allows 2N Different Functions
ECE 120: Introduction to Computing © 2016 Steven S. Lumetta. All rights reserved. slide 5
Using x’s for outputs means allowing more
than one function to be chosen.
Each x can become a 0 or a 1.
So optimizing with N x’s means
choosing from among 2N possible functions.
An Example with Two “Don’t Cares”
ECE 120: Introduction to Computing © 2016 Steven S. Lumetta. All rights reserved. slide 6
Let’s do an example.
The function F appears
to the right, partially
specified.
Let’s say that we don’t
care about the value of F
when AB=01.*
*This notation means A=0 AND B=1. You can infer that
AB in this case does not mean A AND B because
the product AB has a single truth value (0 or 1).
F
AB
00 01 11 10
C
0 0 1 0
1 1 1 1
Solution for F with 0s: AB + B’C
ECE 120: Introduction to Computing © 2016 Steven S. Lumetta. All rights reserved. slide 7
One option is to fill the
blanks with 0s.*
Then we can solve.
F = AB + B’C
But we could have chosen
values other than 0, too.
*Without more information about F, filling with 0s
is no better nor worse than any other choice.
F
AB
00 01 11 10
C
0 0 1 0
1 1 1 1
0
0
Solution for F with a 0 and a 1: AB + C
ECE 120: Introduction to Computing © 2016 Steven S. Lumetta. All rights reserved. slide 8
For example, we could
put a 0 and a 1…
And then solve.
F = AB + C
This function is better
than the first one
(it has one fewer literal).
F
AB
00 01 11 10
C
0 0 1 0
1 1 1 1
0
1
9/12/2016
Solution for F with “Don’t Cares”: B + C
ECE 120: Introduction to Computing © 2016 Steven S. Lumetta. All rights reserved. slide 9
Rather than solving
for all four possibilities,
let’s write x’s into the
K-map.
The x’s can be 0s or 1s,
so to solve the K-map,
◦we can grow loops to include x’s,
◦but we do not need to cover x’s.
F = B + C (the best possible answer)
F
AB
00 01 11 10
C
0 0 1 0
1 1 1 1
x
x
Always Check that “Don’t Cares” Have No Ill Effects
ECE 120: Introduction to Computing © 2016 Steven S. Lumetta. All rights reserved. slide 10
When designing with x’s,
it’s a good habit to verify
that the 0s and 1s
generated in place of x’s
do not cause any adverse
effects.
For our function, both x’s
become 1s because they are inside a loop.
(We don’t have any more context for this
example, so we are done.)
F
AB
00 01 11 10
C
0 0 1 0
1 1 1 1
x
x
1
1
