Biomedical Engineering Reference
In-Depth Information
Table
4.2
Truth table for
f
B
f
B
x
1
x
2
=
x
1
x
2
0
0
0
0
1
1
1
0
0
1
1
0
Table
4.
3
T
ruth table for
g
B
g
B
x
1
x
2
=
x
1
x
2
+
x
1
x
2
0
0
1
0
1
0
1
0
0
1
1
1
The truth tables for
f
B
and
g
B
are shown in Tables
4.2
and
4.3
. We select the
appropriate coefficients to find the corresponding Zhegalkin functions are:
f
Z
=
x
2
−
x
1
x
2
g
Z
=
1
−
x
1
−
x
2
+
2
x
1
x
2
Plotting the Zhegalkin functions as a surface plot, we observe in Figs.
4.1
and
4.2
that the corner points (where the inputs are 0 or 1) match the Boolean function output
1
0.8
0.6
f
0.4
1
0.2
0.8
0
0.6
0
0.2
x
2
0.4
0.4
0.6
0.2
x
1
0.8
0
1
Fig. 4.1
Zhegalkin function
f
Z
x
1
x
2
for Boolean function
f
B
=
x
2
−
=
x
1
x
2
