!
"#
$
"
#%
!
&"
'(
!
!
*+
,.
(/
,0.
*($
,
,
,.
,%
X
Y
Z
X
Y
Z
X
0
0
1
1
Y
0
1
0
1
Z
0
0
0
1
X
0
0
1
1
Y
0
1
0
1
Z
0
1
1
1
X
Y
X
0
1
Y
1
0
X
Y
X
0
1
Y
0
1
)
* *+
X•Y
*(/
X+Y
,(/
X⊕Y
,*(/
X⊕Y
XY
!
1 %2
X
Y
Z
X
0
0
1
1
Y
0
1
0
1
Z
1
1
1
0
Z
X
0
0
1
1
Y
0
1
0
1
Z
1
0
0
0
X
0
0
1
1
Y
0
1
0
1
Z
0
1
1
0
X
0
0
1
1
Y
0
1
0
1
Z
1
0
0
1
X
Y
X
Y
Z
X
Y
Z
+
!
3
* 34
!
5
*
3
!
!
6
7 3$! 8
"
6
7
3$! 8
1
#
5
!
5
2
' ""
"
" 36 : 1- 2
%0 +
NAND2
OR2
19
AND2
+
17
6
16
" 36 : 10 2
%
NOR2
AND2
21
22
6
9
"3
7
#
#
&" 3
( " 3
#
7
#
7
: << 0 <
: <
0
<0
< 0
< <0
<0
;
6
3
=
: << 0 <
0
=
: 1⊕ 2⊕
<
< <0
AND3
<
<
28
XOR
AND3
OR4
<
XOR
32
< 30
AND3
33
27
<
< 29
AND3
31
6
3
#7
=
: <
0
=
0
<
<0
:
0
0
AND3
<
AND2
1
AND3
<
OR4
2
AND3
<3
AND3
5
11
AND2
OR3
12
14
AND2
13
4
>
@ 5
3 )7
A
XOR
32
"" 7
#
B
A1 B1
A2 B2
Cin Cout
Cin Cout
Sum1
Sum2
1-Bit Adder
XOR
0
33
AND2
Cin
Cout
11
AND2
OR3
12
14
AND2
13
Overflow
Sum
?
' ""
A5
4
'
+
!
!
!
= !
"
"
6: % %
0 % 0 %0
: %1%
0 2
0 1%
0 2
: %0
AND2
<
26
AND2
25
OR2
24
6
' #"
' #
""
#
" "
" 3 Z = A • B • (C + D ) = A • B • ( C + D )
A
A
B
Z
C
D
Z
B
C
D
4!
4
Z
! "
=
!
C" =D
+
B
!
5#
/
/
/
!
!
E
" B
B
5 B
"
!
B
+
"
=
=
3/
3'
= "
F
"
="
#
)
'
4
"
#
*($ *(/
* *+
" 31
,
.2:
&
1
,
!
*($ G * *+
* *+
,
,
*(/
*(/
.:
.:
.2
#*(/
"
3
1
1 ,2
1
1 ,2
'
#* *+
!
"
1
1
!
!
.2
2
.2
2
'(
'(
!
"
0V ≡ Logic 0
1.8V ≡ Logic 1
#
#'
7
X
(
$
5
Y
7
!
J
>K
X
Y
0V
1.8V
1.8V 0V
J
>K
0.13Im
' H !
&
K
K
'
7 "
'(
5
A * *+ *(/ *($
+ %
*+ (/
J
>K
X
Y
J
>K
J
>K
J
>K
Z
X
0
0
1
1
Y
0
1
0
1
Z
1
1
1
0
K
K
9