12/1/2008
1
A=B
Karnaugh map does not simplify
A=B
WX
\
YZ
00
01
11
10
Karnaugh map does not simplify
expression
But, look at two terms in expression:
WX
\
YZ
00
01
11
10
00 1
1
But, look at two terms in expression:
F
=
W’X’Y’Z’
+
W’XY’Z
+
.......
01
1
11
1
F
A=B
=
W’X’Y’Z’
+
W’XY’Z
+
.......
= W’Y’(X’Z’ + XZ) +
.......
11
1
10
1
= W’Y’(X’Z’ + XZ) +
.......
= W’Y’(X’ XOR Z) +
.......
1
= W’Y’(X’ XOR Z) +
.......
F
A=B
=
W’Y’(X XOR Z’) +
.......
Or, equivalently:
F
A=B
=
W’Y’(X XOR Z’) +
Or, equivalently:
Recall
:
X
XOR
Y= XY’ + X’Y => X’
XOR
Y= X’Y’ + XY
Recall
:
X
XOR
Y= XY’ + X’Y => X’
XOR
Y= X’Y’ + XY
+V
X’
X
X’
=
Also:
X
X’
X
X’
=
Also:
OTHER COMBINATIONAL COMPONENTSOTHER COMBINATIONAL COMPONENTS
OTHER COMBINATIONAL COMPONENTSOTHER COMBINATIONAL COMPONENTS
Recall definition of
combinational logic
: current output(s) depend
only on current input(s)
Recall definition of
combinational logic
: current output(s) depend
only on current input(s)
This is different from
sequential logic
, where the output depends on
This is different from
sequential logic
, where the output depends on
current input(s) and previous input(s) and/or output(s). Sequential
logic involves
memory
, where combinational logic does not.
logic involves
memory
, where combinational logic does not.
Multiplexer
(MUX):
A multiplexer acts like a switch
-
it routes
Multiplexer
(MUX):
A multiplexer acts like a switch
-
it routes
(connects) the appropriate input to the output according to the input
address
If a particular input line is addressed, the
address
A0
If a particular input line is addressed, the
output will be at the same logic level as
.
A0
A1
A2
If the address has M bits, the MUX can
output will be at the same logic level as
that input
Output
.
.
A2
AN
If the address has M bits, the MUX can
route up to 2
M
inputs
Output
route up to 2
inputs
MUXes
can be built with logic gates
Address
MUXes
can be built with logic gates
