Nama : M.Agung
NPM : 011170007
Tugas Tambahan
1. Buktikan apakah M,N + M.' N + M.'N' = M'+N
2. Buktikan apakah p'q + p + q' = p' q'
3. Sederhanakan fungsi F ( p,q ) = p'q dan F ( M,N,O,) = MNO' + MN'O + M'NO + MNO kemudian nyatakan kedalam gerbang logika
NPM : 011170007
Tugas Tambahan
1. Buktikan apakah M,N + M.' N + M.'N' = M'+N
2. Buktikan apakah p'q + p + q' = p' q'
3. Sederhanakan fungsi F ( p,q ) = p'q dan F ( M,N,O,) = MNO' + MN'O + M'NO + MNO kemudian nyatakan kedalam gerbang logika
Jawab no 1
M
|
N
|
M’
|
N’
|
M,N
|
M.’N
|
M.’N’
|
=M’+N
|
M,N + M.’N
|
+M.’N’ = M’+N
|
M,N+M.’N+M’.N’=M’+N
|
0
|
0
|
1
|
1
|
1
|
1
|
0
|
0
|
1
|
0
|
0
|
0
|
0
|
1
|
1
|
0
|
1
|
0
|
0
|
1
|
0
|
0
|
0
|
1
|
1
|
0
|
0
|
0
|
1
|
0
|
0
|
1
|
0
|
0
|
1
|
1
|
0
|
0
|
0
|
1
|
0
|
0
|
1
|
0
|
1
|
0
|
0
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
0
|
0
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
0
|
0
|
1
|
1
|
1
|
0
|
1
|
1
|
1
|
1
|
1
|
0
|
0
|
1
|
1
|
1
|
0
|
1
|
1
|
1
|
Jawab no 2
p
|
q
|
P’
|
q’
|
P’q
|
P+q’
|
=p’q’
|
P’q
+p+q’ = p’q’
|
0
|
0
|
1
|
1
|
0
|
0
|
1
|
1
|
0
|
0
|
1
|
1
|
0
|
0
|
1
|
1
|
0
|
1
|
1
|
0
|
1
|
0
|
0
|
1
|
0
|
1
|
1
|
0
|
1
|
0
|
0
|
1
|
1
|
0
|
0
|
1
|
0
|
1
|
0
|
1
|
1
|
0
|
0
|
1
|
0
|
1
|
0
|
1
|
1
|
1
|
0
|
0
|
0
|
0
|
0
|
0
|
1
|
1
|
0
|
0
|
0
|
0
|
0
|
0
|
Jawab no 3
F (p , q ) = p’ q F (M,N,O) = MNO’ +MN’O + M’NO +MNO
= p ‘ +
q = MN (O’ + O) + MN (
O’+O )
= q + p’ = MN (1)+ MN (1)
= q + p
=
MN + MN + (1+1)
= qp = MN + MN
= (M + M ) + ( N + N )
= 1 + 1
=
1
Gerbang logika F (p , q ) = p’ q


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