Maximum and minimum items
1. Definition
1. Minimum term: the term containing n variables
Minimum itemexpression：
F
=
A
‾
B
C
+
A
B
‾
C
+
A
B
C
‾
F=\overline{A}BC+A\overline{B}C+AB\overline{C}
F=ABC+ABC+ABC
=
m
3
+
m
5
+
m
6
+
m
7
~~~~=m_3+m_5+m_6+m_7
=m3+m5+m6+m7
=
Σ
m
(
3
,
5
,
6
,
7
)
~~~~=\Sigma m(3,5,6,7)
=Σm(3,5,6,7)
2. Maximum term: or term containing n variables
Maximum term expression:
F
=
(
A
‾
+
B
‾
+
C
‾
)
(
A
‾
+
B
‾
+
C
)
(
A
+
B
‾
+
C
‾
)
F=(\overline{A}+\overline{B}+\overline{C})(\overline{A}+\overline{B}+C)(A+\overline{B}+\overline{C})
F=(A+B+C)(A+B+C)(A+B+C)
=
M
0
M
1
M
2
N
4
~~~~=M_0M_1M_2N_4
=M0M1M2N4
=
Π
M
(
0
,
1
,
2
,
4
)
~~~~=\Pi M(0,1,2,4)
=ΠM(0,1,2,4)
2. Relationships and Properties
M i = m i ′ M_i= m_i' Mi=mi′
The sum of all minimum terms is always 1
The product of any two smallest terms is always 0
For any set of inputs, only the only minimum term is 1.
The product of all the largest terms is always 0
The sum of any two largest terms is always 1
For any set of inputs, only the only maximum term is 0.