Penyerdehanakan gerbang Kombinasi ( combinational Gate )

Penyerdehanakan gerbang Kombinasi ( combinational Gate ) 

Sederhanakan Soal Latihan Berikut :

        1.      Y = A’ C’ + A B C’

        2.      Y = A’ B’ C D’ + A’ B’C’ D’

        3.      Y = A’ D + A B D

        4.      Y = ( A’ + B ) ( A + B )

 

  Jawab :

1.  Y=A' C' + A B C'

   Y=(A' A) C' + B C'

   Y=A' C' + B C'

   TABEL

A	B	A’	C’	B C’	A’ C’	A’ C’ + B C
0	0	1	1	1	0	1
0	0	1	0	0	0	0
0	1	1	1	1	1	1
0	1	1	0	0	0	0
1	0	0	1	0	0	0
1	0	0	0	0	0	0
1	1	0	1	0	1	1
1	1	0	0	0	0	0

1.      Y = A’ C’ + A B C’

Y = ( A’ A ) C’ + B C’

Y = A’ C’ + B C’

Tabel :

A	B	A’	C’	B C’	A’ C’	A’ C’ + B C
0	0	1	1	1	0	1
0	0	1	0	0	0	0
0	1	1	1	1	1	1
0	1	1	0	0	0	0
1	0	0	1	0	0	0
1	0	0	0	0	0	0
1	1	0	1	0	1	1
1	1	0	0	0	0	0

2.      Y = A’ B’ C D’ + A’ B’ C’ D’

Y = ( A’ + A ) ( B’ + B’ ) ( C + C’ ) ( D’ + D’ )

Y = A’ B’ 0 D’

Y = A’ B’ D’

Tabel :

C	A’	B’	C’	D’	A’ B’ D’
0	1	1	1	1	1
0	1	1	1	0	0
1	1	1	0	1	1
1	1	1	0	0	0
0	1	0	1	1	0
0	1	0	1	0	0
1	1	0	0	1	0
1	1	0	0	0	0
0	0	1	1	1	0
0	0	1	1	0	0
1	0	1	0	1	0
1	0	1	0	0	0
0	0	0	1	1	0
0	0	0	1	0	0
1	0	0	0	1	0
1	0	0	0	0	0

                       

3.      Y = A’ D + A B D

Y = ( A’ A ) D + B D

Y = A’ D + B D

Tabel :

A	B	D	A’	A’ D	A B D	A’ D + A B D
0	0	0	1	0	0	0
0	0	1	1	1	0	1
0	1	0	1	0	0	0
0	1	1	1	1	1	1
1	0	0	0	0	0	0
1	0	1	0	0	0	0
1	1	0	0	0	0	0
1	1	1	0	0	1	1

4.      Y = ( A’ +  B ) ( A + B )

Y = ( A’ A + A’ B ) ( B A + B B )

Y = ( A’ + A B ) ( B A + B )

Y = ( A’ + B ) B

Tabel  :

A	B	A’	A’ + B	( A’ + B ) B
1	1	0	1	1
1	0	0	0	0
0	1	1	1	1
0	0	1	1	0