Sistem Bilangan yang sering dipakai sistem digital

Nama : M.Agung
NPM : 011170007

Tugas : Melengkapi tugas

1. Diketahui tabel kebenaran sbb:

A	B	B	Y
0	0	0	1
0	0	1	0
0	1	0	1
0	1	1	1
1	0	0	0
1	0	1	1
1	1	0	1
1	1	1	0

    Tentukan pernyataan logikanya dan buatlah rangkaian logikanya

   

   Jawabnya :          

Y   = A’B’C’ + A’BC’ + A’BC + AB’C + ABC’

     = A’C’ (B’ + B) + A’BC + AB’C + ABC’

     = A’C’ + ABC + A’BC + ABC + AB’C +ABC + ABC’ + ABC

     = A’C’ + ABC + BC (A’ + A) + AC (B’ + B) + AB (C’ + C)

     = A’C’ + ABC + BC + AC + AB

     = A’C’ + AB ( C + 1) + BC + AC

     = A’C’ + AB + BC + AC

2. Buatlah tabel kebenaran dari fungsi

    F(A,B,C,D) = B'C + AC'D  + B'D, kemudian

    ekspresikanlah menjadi SOP dan POS, lalu buatlah rangkaian logikanya

  

Jawabnya:

   

A	B	C	D	A’	B’	C’	B’C’	AC’	AC’D	B’D	B’C’ + AC’D	B’C’ + AC’D + B’D
0	0	0	0	1	1	1	1	0	0	0	1	1
0	0	0	1	1	1	1	1	0	0	1	1	1
0	0	1	0	1	1	0	0	0	0	0	0	0
0	0	1	1	1	1	0	0	0	0	1	0	1
0	1	0	0	1	0	1	0	0	0	0	0	0
0	1	0	1	1	0	1	0	0	0	0	0	0
0	1	1	0	1	0	0	0	0	0	0	0	0
0	1	1	1	1	0	0	0	0	0	0	0	0
1	0	0	0	0	1	1	1	1	0	0	1	1
1	0	0	1	0	1	1	1	1	1	1	1	1
1	0	1	0	0	1	0	0	0	0	0	0	0
1	0	1	1	0	1	0	0	0	0	1	0	1
1	1	0	0	0	0	1	0	1	0	0	0	0
1	1	0	1	0	0	1	0	1	1	0	1	1
1	1	1	0	0	0	0	0	0	0	0	0	0
1	1	1	1	0	0	0	0	0	0	0	0	0

SOP = A’B’C’ + A’B’C’ + A’B’C + AB’C’ + AB’C’ + AB’C + ABC’

POS = (A’+B’+C).(A’+B+C’).(A’+B+C’).(A’+B+C).(A’+B+C).(A+B’+C).(A+B+C’).(A+B+C).            (A+B+C)

F(A,B,C,D) = B’C’ + B’D + AC’D